Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 4 - Quadratic Functions and Equations - 4-6 Complete the Square - Practice and Problem-Solving Exercises - Page 237: 35

Answer

$\left\{6-\sqrt{29}, 6+\sqrt{29}\right\}$

Work Step by Step

Subtract $7$ to both sides to obtain: $$x^2-12x=-7$$ RECALL: To complete the square for $x^2 +mb$, just add $\left(\dfrac{m}{2}\right)^2$. Use the rule above to complete the square (note that to retain the equality, whatever is added on th left side of the equation must also be added to the right side of the equation) and obtain: \begin{align*} x^2-12x+\left(\frac{-12}{2}\right)^2&=-7+\left(\frac{-12}{2}\right)^2\\\\ x^2-12x+\left(-6\right)^2&=-7+\left(-6\right)^2\\\\ x^2-12x+36&=-7+36\\\\ (x-6)^2&=29 \end{align*} Take the square root of both sides to obtain: \begin{align*} \sqrt{(x-6)^2}&=\pm \sqrt{29}\\\\ x-6&=\pm \sqrt{29}\\\\ x&=6\pm \sqrt{29}\\\\ \end{align*} Thus, the solutions are: $\left\{6-\sqrt{29}, 6+\sqrt{29}\right\}$
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