Big Ideas Math - Algebra 1, A Common Core Curriculum

Published by Big Ideas Learning LLC
ISBN 10: 978-1-60840-838-2
ISBN 13: 978-1-60840-838-2

Chapter 9 - Solving Quadratic Equations - 9.4 - Solving Quadratic Equations by Completing the Square - Exercises - Page 512: 34

Answer

The third step is wrong, and the correct answer is $x^2-x+\frac{1}{4}=2+\frac{1}{4}$.

Work Step by Step

The given equation is $\Rightarrow 2x^2-2x-4=0$ Add $4$ to each side. $\Rightarrow 2x^2-2x-4+4=0+4$ Simplify. $\Rightarrow 2x^2-2x=4$ Divide each side by $2$. $\Rightarrow x^2-x=2$ Find the value of $(\frac{b}{2})^2$. Substitute $-1$ for $b$. $=(\frac{-1}{2})^2$ Simplify. $=\frac{1}{4}$ Add $\frac{1}{4}$ to each side of the equation. $\Rightarrow x^2-x+\frac{1}{4}=2+\frac{1}{4}$ Hence, the third step is wrong, and the correct answer is $x^2-x+\frac{1}{4}=2+\frac{1}{4}$.
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