Question

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

Answer 1

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`