Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 8 - Section 8.3 - Solving Equations by Using Quadratic Methods - Exercise Set: 35

Answer

The solution of the given equation is $3$.

Work Step by Step

Square both sides to obtain: $(2x)^2=(\sqrt{11x+3})^2 \\4x^2=11x+3 \\4x^2-11x-3=0$ Factor the trinomial: $(4x+1)(x-3)=0$ Use the Zero Factor Property by equating each factor to zero, then solve each equation to obtain: \begin{array}{ccc} \\&4x+1=0 &\text{or} &x-3=0 \\&4x=-1 &\text{or} &x=3 \\&x=-\frac{1}{4} &\text{or} &x=3 \end{array} Note that when $x=-\frac{1}{4}$: the left side of the given equation becomes $-\frac{1}{2}$. Since the right side of the given equation involves a principal square root, its value must be non-negative. Thus, $-\frac{1}{4}$ is not a solution of the equation. Therefore, the solution of the given equation is $3$.
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