Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 9 - Section 9.1 - Solving Quadratic Equations by the Square Root Property - Exercise Set: 64

Answer

$x=\frac{\sqrt{ab}}{a}$

Work Step by Step

To solve for x, isolate x on one side of the equation. $ax^2-b=0$ Add b to both sides. $ax^2-b+b=0+b$ Simplify. $ax^2=b$ Divide both sides by a. $\frac{ax^2}{a}=\frac{b}{a}$ Simplify. $x^2=\frac{b}{a}$ Take the square root of each side. $\sqrt{x^2}=\sqrt{\frac{b}{a}}$ Simplify. $x=\sqrt{\frac{b}{a}}$ Rationalize the denominator. $x=\sqrt{\frac{b}{a}}=\frac{\sqrt b}{\sqrt a}=\frac{\sqrt b\times \sqrt a}{\sqrt a\times\sqrt a}=\frac{\sqrt{ab}}{a}$
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