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Solving Equations by Completing the Square

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Lesson Plans and Worksheets for Algebra I
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Common Core For Algebra I

Examples, solutions, and videos to help Algebra I students learn how to solve complex quadratic equations, including those with a leading coefficient other than 1, by completing the square. Some solutions may be irrational. Students draw conclusions about the properties of irrational numbers, including closure for the irrational number system under various operations.

New York State Common Core Math Algebra I, Module 4, Lesson 13

Worksheets for Algebra 1

Lesson 13 Summary

When a quadratic equation is not conducive to factoring, we can solve by completing the square. Completing the square can be used to find solutions that are irrational, something very difficult to do by factoring.

1. The leading coefficient of x2 must be 1
2. Move the constant (c) so that the variables are isolated
3. Take half the (b) coefficient. Square it and add it to both sides
4. Rewrite the equation as perfect square binomial
5. Solve for x

Example 1

Solve for x:
x2 - 2x = 12
1/2 r2 - 6r = 2

The sum or product of two rational numbers is always a rational number.
The sum of a rational number and an irrational number is always an irrational number.
The product of a rational number and an irrational number is an irrational number as long as the rational number is not zero.

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