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 238: 59

Answer

\begin{align*}k&=-1 &\text{ or }& &k=1\end{align*}.

Work Step by Step

RECALL: To complete the square of $x+kx$, we add $\left(\dfrac{k}{2}\right)^2$ to obtain: $$x^2+kx+\dfrac{k^2}{4}$$ Thus, to find the value of $k$, we simply equate the constant term of the given expressions to $\dfrac{k^2}{4}$. Hence, \begin{align*} \dfrac{k^2}{4}&=\frac{1}{4}\\\\ k^2&=4\left(\frac{1}{4}\right)\\\\ k^2&=1\\\\ k&=\pm\sqrt{1}\\\\ k&=\pm 1 \end{align*} Thus, $k=-1 \text{ or } k=1$.
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