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Resources to Help You Solve Math Equations
Whether you love math or suffer through every single problem, there are plenty of resources to help you solve math equations. Skip the tutor and log on to load these awesome websites for a fantastic free equation solver or simply to find answers for solving equations on the Internet.
Stand By for Automatic Math Solutions at Quick Math
The Quick Math website offers easy answers for solving equations along with a simple format that makes math a breeze. Load the website to browse tutorials, set up a polynomial equation solver, or to factor or expand fractions. From algebra to calculus and graphs, Quick Math provides not just the answers to your tough math problems but a step-by-step problem-solving calculator. Use the input bar to enter your equation, and click on the “simplify” button to explore the problem and its solution. Choose some sample problems to practice your math skills, or move to another tab for a variety of math input options. Quick Math makes it easy to learn how to solve this equation even when you’re completely confused.
Modern Math Answers Come From Mathway
Mathway offers a free equation solver that sifts through your toughest math problems — and makes math easy. Simply enter your math problem into the Mathway calculator, and choose what you’d like the math management program to do with the problem. Pick from math solutions that include graphing, simplifying, finding a slope or solving for a y-intercept by scrolling through the Mathway drop-down menu. Use the answers for solving equations to explore different types of solutions, or set the calculator to offer the best solution for your particular math puzzle. Mathway offers the option to create an account, to sign in or sign up for additional features or to simply stick with the free equation solver.
Wyzant — Why Not?
Wyzant offers a variety of answers when it comes to “how to solve this equation” questions. Sign up to find a tutor trained to offer online sessions that increase your math understanding, or jump in with the calculator that helps you simplify math equations. A quick-start guide makes it easy to understand exactly how to use the Wyzant math solutions pages, while additional resources provide algebra worksheets, a polynomial equation solver, math-related blogs to promote better math skills and lesson recording. Truly filled with math solutions, Wyzant provides more than just an equation calculator and actually connects you with people who are trained to teach the math you need. Prices for tutoring vary greatly, but access to the website and its worksheets is free.
Take in Some WebMath
Log onto the WebMath website, and browse through the tabs that include Math for Everyone, Trig and Calculus, General Math and even K-8 Math. A simple drop-down box helps you to determine what type of math help you need, and then you easily add your problem to the free equation solver. WebMath provides plenty of options for homeschoolers with lesson plans, virtual labs and family activities.
Khan Academy Offers More Than Answers
A free equation solver is just the beginning when it comes to awesome math resources at Khan Academy. Free to use and filled with videos that offer an online teaching experience, Khan Academy helps you to simplify math equations, shows you how to solve equations and provides full math lessons from Kindergarten to SAT test preparation. Watch the video for each math problem, explore the sample problems, and increase your math skills right at home with Khan Academy’s easy-to-follow video learning experience. Once you’ve completed your math video, move onto practice problems that help to increase your confidence in your math skills.
MORE FROM QUESTIONSANSWERED.NET
- List of Lessons
- 1.1 Return to Algebra
- 1.2 Linear Inequalities
- 1.3 Absolute Value
- 1.4 Rewriting Equations
- Unit 1 Review
- Unit 1 Algebra Skillz Review
- 2.1 Function Notation
- 2.2 Functions/Relations
- 2.3 Slope and Rate of Change
- 2.4 Graphing Lines
- 2.5 Write Equations of Lines
- Unit 2 Review
- Unit 2 Algebra Skillz and SAT Review
- 3.1 Absolute Value Inequality
- 3.2 Absolute Value Graphs
- 3.3 Piecewise Functions
- Unit 3 Review
- Unit 3 Algebra Skillz
- 4.1 Solving Systems by Graphing
- 4.2 Solving Systems Algebraically
- 4.3 Systems of Inequalities
- Unit 4 Review
- 5.1 Graph in Vertex Form
- 5.2 Graph in Standard Form
- 5.3 Solve by Factoring
- 5.4 GCF and DoS
- 5.5 Solving by Square Roots
- Unit 5 Review
- Unit 5 Algebra Skillz and SAT Review
- 6.1 Imaginary and Complex Numbers
- 6.2 Operations on Complex Numbers
- 6.3 Completing the Square
- 6.4 Quadratic Formula
- Unit 6 Review
- Unit 6 Algebra Skillz
- SEMESTER EXAM
- 7.1 Properties of Exponents
- 7.2 Polynomial Division
- 7.3 Solving Polynomial Functions by Factoring
- 7.4 Graphs of Polynomial Functions
- 8.1 Evaluate Nth Roots
- 8.2 Properties of Rational Exponents
- 8.3 Function Operations and Composition
- 8.4 Inverse Operations
- 8.5 Graph Square and Cube Root Functions
- 8.6 Solving Radical Equations
- Unit 8 Review
- Unit 8 Algebra Skillz and SAT Review
- 9.1 Exponential Growth
- 9.2 Exponential Decay
- 9.3 The Number e
- 9.4 Intro to Logarithms
- 9.5 Properties of Logarithms
- 9.6 Solve Exponential and Log Equations
- Unit 9 Review
- Unit 9 Algebra Skillz
- 10.1 Graph Rational Functions
- 10.2 Multiply and Divide Rational Expressions
- 10.3 Add and Subtract Rational Expressions
- 10.4 Solve Rational Equations
- Unit 10 Review
- Unit 10 Algebra Skillz
- 11.1 Parabolas
- 11.2 Ellipses and Circles
- 11.3 Hyperbolas
- 11.4 Classifying Conics
- Unit 11 Review
- Unit 11 Algebra Skillz
- 12.1 Matrix Operations
- 12.2 Matrix Multiplication
- 12.3 Inverse Matrices
- 12.4 Encoding Messages
- Unit 12 Review
- SEMESTER 2 EXAM
- Teacher Resources
Section 6.3 Completing the Square
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- Study Skills Quiz
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Solving Quadratic Equations by Completing the Square
Factoring Roots Completing the Square Formula Graphing Examples
The quadratic equation in the previous page's last example was:
( x − 2) 2 − 12 = 0
The expression on the left-hand side of this equation can be multiplied out and simplified to be:
x 2 − 4 x − 8
But we still would not have been able to solve the equation, even with the quadratic formatted this way, because it doesn't factor and it isn't ready for square-rooting.
Content Continues Below
Completing the Square
The only reason we could solve it on the previous page was because they'd already put all the x stuff inside a square, so we could move the strictly-numerical portion of the equation to the other side of the "equals" sign and then square-root both sides. They won't always format things as nicely as this. So how do we go from a regular quadratic like the above to an equation that is ready to be square-rooted?
We will have to "complete the square".
Here's how we'd have solved the last equation on the previous page, if they hadn't formatting it nicely for us.
Use completing the square to solve x 2 − 4 x − 8 = 0.
As noted above, this quadratic does not factor, so I can't solve the equation by factoring. And they haven't given me the equation in a form that is ready to square-root. But there is a way for me to manipulate the quadratic to put it into that ready-for-square-rooting form, so I can solve.
First, I put the loose number on the other side of the equation:
x 2 − 4 x − 8 = 0
x 2 − 4 x = 8
Then I look at the coefficient of the x -term, which is −4 in this case. I take half of this number ( including the sign ), which gives me −2 . (I need to keep track of this value. It will simplify my work later on.)
Then I square this value to get +4 , and add this squared value to both sides of the equation:
x 2 − 4 x + 4 = 8 + 4
x 2 − 4 x + 4 = 12
This process creates a quadratic expression that is a perfect square on the left-hand side of the equation. I can factor, or I can simply replace the quadratic with the squared-binomial form, which is the variable, x , together with the one-half number that I got before (and noted that I'd need later), which was −2 . Either way, I get the square-rootable equation:
( x − 2 ) 2 = 12
(I know it's a " −2 " inside the parentheses because half of −4 was −2 . By noting the sign when I'm finding one-half of the coefficient, I help keep myself from messing up the sign later, when I'm converting to squared-binomial form.)
(By the way, this process is called "completing the square" because we add a term to convert the quadratic expression into something that factors as the square of a binomial; that is, we've "completed" the expression to create a perfect-square binomial.)
Now I can square-root both sides of the equation, simplify, and solve:
Using this method, I get the same answer as I had before; namely:
Solve 2 x 2 − 5 x + 1 = 0 by completing the square.
There is one extra step for solving this equation, because the leading coefficient is not 1 ; I'll first have to divide through to convert the leading coefficient to 1 . Here's my process:
2 x 2 − 5 x + 1 = 0
x 2 − (5/2) x + 1/2 = 0
x 2 − (5/2) x = −(1/2)
Now that I've got all the terms with variables on one side, with the strictly-numerical term on the other side, I'm ready to complete the square on the left-hand side. First, I take the linear term's coefficient (complete with its sign), −(5/2) , and multiply by one-half, and square:
(1/2) × [−(5/2)] = −(5/4)
( −(5/4) ) 2 = 25/16
Then I add this new value to both sides, convert to squared-binomial form on the left-hand side, and solve:
x 2 − (5/2) x + 25/16 = −(1/2) + 25/16
( x − 5/4 ) 2 = 17/16
sqrt[( x − 5/4) 2 ] = ± sqrt[17/16]
x − 5/4 = ± sqrt/4
x = 5/4 ± sqrt/4
The two terms on the right-hand side of the last line above can be combined over a common denominator, and this is often ("usually"?) how the answer will be written, especially if the instructions for the exercise included the stipulation to "simplify" the final answer:
x = (5 ± sqrt)/4
Elsewhere , I have a lesson just on solving quadratic equations by completing the square. That lesson (re-)explains the steps and gives (more) examples of this process. It also shows how the Quadratic Formula can be derived from this process. If you need further instruction or practice on this topic, please read the lesson at the above hyperlink.
By the way, unless you're told that you have to use completing the square, you will probably never use this method in actual practice when solving quadratic equations. Either some other method (such as factoring) will be obvious and quicker, or else the Quadratic Formula (reviewed next ) will be easier to use. However, if your class covered completing the square, you should expect to be required to show that you can complete the square to solve a quadratic on the next test.
You can use the Mathway widget below to practice solving quadratic equations by completing the square. Try the entered exercise, or type in your own exercise. Then click the button and select "Solve by completing the square" to compare your answer to Mathway's. (Or skip the widget and head to the next page.)
Please accept "preferences" cookies in order to enable this widget.
(Click "Tap to view steps" to be taken directly to the Mathway site for a paid upgrade.)
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The four steps for solving an equation include the combination of like terms, the isolation of terms containing variables, the isolation of the variable and the substitution of the answer into the original equation to check the answer.
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Whether you love math or suffer through every single problem, there are plenty of resources to help you solve math equations. Skip the tutor and log on to load these awesome websites for a fantastic free equation solver or simply to find an...
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