## Algebra 1

Published by Prentice Hall

# Chapter 9 - Quadratic Functions and Equations - 9-5 Completing the Square - Practice and Problem-Solving Exercises - Page 565: 43

#### Answer

To complete the square, we will add $\dfrac{25}{16}$ on both sides. Roots of $x$ are: $x=0.64, -3.14$

#### Work Step by Step

$4x^2+10x=8$ or, $x^2+\frac{10}{4}x=2$ Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=\frac{10}{4}$ To complete the square, add $\dfrac{25}{16}$ on both sides. $x^2+\dfrac{10}{4}x+\dfrac{25}{16}=2+\dfrac{25}{16}$ $\implies (x+\dfrac{5}{4})^2=\dfrac{57}{16}$ $\implies (x+1.25)^2=3.56$ $\implies (x+1.25)=1.89$ and $\implies (x+1.25)=-1.89$ or, $x=0.64, -3.14$ To complete the square, we will add $\dfrac{25}{16}$ on both sides. Roots of $x$ are: $x=0.64, -3.14$

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