we have
\(x^{2} = -13x- 4\)
to find the solution let's factor the equation
Group terms that contain the same variable, and move the constant to the opposite side of the equation
\(x^{2} +13x=- 4\)
Complete the square. Remember to balance the equation by adding the same constants to each side
\(x^{2} +13x+42.25=- 4+42.25\)
\(x^{2} +13x+42.25=38.25\)
Rewrite as perfect squares
\((x+6.5)^{2}=38.25\)
\((x+6.5)=(+/-)\sqrt{38.25}\\ x1=-6.5+\sqrt{38.25}\\ x2=-6.5-\sqrt{38.25}\)
\(x1=-6.5+\sqrt{38.25}\\ x1=-0.315\)
\(x2=-6.5-\sqrt{38.25}\\ x2=-12.685\)
therefore
the answer is
the solutions of the equation are
\(x1=-0.315\\ x2=-12.685\)
