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- 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
- FlippedMath.com
- Teacher Resources

## Section 6.3 Completing the Square

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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:

The expression on the left-hand side of this equation can be multiplied out and simplified to be:

## MathHelp.com

We will have to "complete the square".

## Use completing the square to solve x 2 − 4 x − 8 = 0.

First, I put the loose number on the other side of the equation:

Then I square this value to get +4 , and add this squared value to both sides of the equation:

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.

x 2 − (5/2) x + 25/16 = −(1/2) + 25/16

sqrt[( x − 5/4) 2 ] = ± sqrt[17/16]

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## Standardized Test Prep

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## IMAGES

## VIDEO

## COMMENTS

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.

Scramble Squares are puzzles involving nine squares. Each side of each square holds half of an image that can be completed if it’s joined to a corresponding side. Most images have a front end and a back end in Scramble Squares.

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...

Solve each equation by completing the square. 1) p. 2 + 14p − 38 = 0. 2) v.

Solve each equation by completing the square. 1) a. 2 + 2a − 3 = 0. 2) a. 2 − 2a − 8 = 0. 3) p. 2 + 16p − 22 = 0.

Solve each equation by completing the square. 1) p² + 14p - 38 = 0. 2.

This algebra 2 video tutorial shows you how to complete the square to solve quadratic equations. This video is for high school students

Solve each equation by completing the square. 1) p² + 14p - 38 = 0. +38 p²+14 + 149].

2 is a perfect square trinomial. To turn the equation given into one that can be

Solving quadratic equations by completing the square ... Choose 1 answer:.

To solve an equation by completing the square requires a couple of extra steps.

1.5 Determine and interpret maximum or minimum values for quadratic equations. A2.5.6 Describe characteristics of quadratic functions and use them to solve real

Demonstrates how to solve quadratics by completing the square, provides a link to a page showing how to "prove" the Quadratic Formula using this method

2016. K ut a Software LLC. A 1 1 rights. Solving Quadratics with Imaginary Solutions. Solve each equation with the quadratic formula. 1) 10x² - 4x + 10 = 0.