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What is the solution set? Select the correct choice below and fill in any answer boxes in your choice

What is the solution set? Select the correct choice below and fill in any answer boxes-example-1
User Mike Peterson
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1 Answer

15 votes
15 votes

Given the equation


\sqrt[]{15-2x}=x

To find the solution of the equation given

By squaring both sides of the equation,


(\sqrt[]{15-2x})^2=(x)^2
\begin{gathered} (\sqrt[]{15-2x})^2=(x)^2 \\ 15-2x=x^2 \end{gathered}

Equating the above equation to zero


\begin{gathered} x^2-(15-2x)=0 \\ x^2-15+2x=0 \\ x^2+2x-15=0 \end{gathered}

Factorizing the above equation


\begin{gathered} x^2+2x-15=0 \\ x^2+5x-3x-15 \\ x(x+5)-3(x+5)=0 \\ (x-3)(x+5)=0 \end{gathered}

The factors of the equation are


\begin{gathered} x-3=0 \\ x=3 \\ x+5=0 \\ x=-5 \\ x=3\text{ or -5} \end{gathered}

Hence, the solution of the set is


-5,3

User Rvf
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2.9k points