Given the equation
[tex]\sqrt[]{15-2x}=x[/tex]
To find the solution of the equation given
By squaring both sides of the equation,
[tex](\sqrt[]{15-2x})^2=(x)^2[/tex][tex]\begin{gathered} (\sqrt[]{15-2x})^2=(x)^2 \\ 15-2x=x^2 \end{gathered}[/tex]
Equating the above equation to zero
[tex]\begin{gathered} x^2-(15-2x)=0 \\ x^2-15+2x=0 \\ x^2+2x-15=0 \end{gathered}[/tex]
Factorizing the above equation
[tex]\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}[/tex]
The factors of the equation are
[tex]\begin{gathered} x-3=0 \\ x=3 \\ x+5=0 \\ x=-5 \\ x=3\text{ or -5} \end{gathered}[/tex]
Hence, the solution of the set is
[tex]-5,3[/tex]
