hello
the question is a quadratic equation and we are asked to use completing the squares method.
to solve this, let's use some basic steps
step 1
divide through the equation by the coefficient of x^2
[tex]\begin{gathered} x^2+4x-60=0 \\ \frac{x^2}{1}+\frac{4x}{1}-\frac{60}{1}=\frac{0}{1} \\ x^2+4x-60=0 \end{gathered}[/tex]step 2
now we have to know that
[tex]\begin{gathered} ax^2+bx+c=0 \\ where\text{ we can relate this to out own equation} \\ x^2+4x-60 \\ a=1,b=4,c=-60 \end{gathered}[/tex][tex]x^2+4x=60[/tex]step 3
complete the square on the left hand side of the equation and balance this by adding the same value on the right hand side of the equation
[tex]\begin{gathered} x^2+4x+4=60+4 \\ (x+2)^2=64 \end{gathered}[/tex]step 4
take the square roots on both sides of the equation
[tex]\begin{gathered} (x+2)^2=64 \\ \sqrt[]{(x+2)^2_{}}=\sqrt[]{64} \\ x+2=\pm8 \\ x=2+8=10 \\ or \\ x=2-8=-6 \end{gathered}[/tex]from the calculations above, the value of x is either 10 or -8