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 511: 19

Answer

$x=3.41$ and $x=0.59$

Work Step by Step

The given equation is $\Rightarrow x^2-4x=-2$ Find the value of $(\frac{b}{2})^2$. Substitute $-4$ for $b$. $=(\frac{-4}{2})^2$ Simplify. $=(-2)^2$ $=4$ Add $4$ to each side of the equation. $\Rightarrow x^2-4x+4=-2+4$ Simplify. $\Rightarrow x^2-4x+4=2$ Write the left side as the square of a binomial. $\Rightarrow (x-2)^2=2$ Take the square root of each side. $\Rightarrow x-2=\pm \sqrt{2}$ Add $2$ to each side. $\Rightarrow x-2+2=\pm \sqrt{2} +2$ Simplify. $\Rightarrow x=\pm \sqrt{2} +2$ The solutions are $x=\sqrt{2} +2=3.41$ and $x=-\sqrt{2} +2=0.59$.
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