## Algebra 1

Published by Prentice Hall

# Chapter 11 - Rational Expressions and Functions - 11-4 Adding and Subtracting Rational Expressions - Mixed Review: 62

#### Answer

$x=6$

#### Work Step by Step

First square both sides: $x^2=5x+6$ Then move the $5x+6$ to the left-hand side to create a quadratic: $x^2-5x-6=0$ Use the quadratic formula to solve for possible values of $x$: The quadratic formula states that for a quadratic $ax^2+bx+c$, the two possible roots take the form $\frac{-b+\sqrt{b^2-4ac}}{2a}$ or $\frac{-b-\sqrt{b^2-4ac}}{2a}$. We see that the two possible roots of our equation are $\frac{5+\sqrt{49}}{2}=6$ and $\frac{5-\sqrt{49}}{2} = -1$. Looking back at our original equation, we see that $x$ is the square root of a number. Because the square root of a number cannot be negative, we see that $x=6$ is the only solution to this equation.

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