we have
[tex] x^{2} = -13x- 4 [/tex]
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
[tex] x^{2} +13x=- 4 [/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex] x^{2} +13x+42.25=- 4+42.25 [/tex]
[tex] x^{2} +13x+42.25=38.25 [/tex]
Rewrite as perfect squares
[tex] (x+6.5)^{2}=38.25 [/tex]
[tex] (x+6.5)=(+/-)\sqrt{38.25}\\ x1=-6.5+\sqrt{38.25}\\ x2=-6.5-\sqrt{38.25} [/tex]
[tex] x1=-6.5+\sqrt{38.25}\\ x1=-0.315 [/tex]
[tex] x2=-6.5-\sqrt{38.25}\\ x2=-12.685 [/tex]
therefore
the answer is
the solutions of the equation are
[tex] x1=-0.315\\ x2=-12.685 [/tex]
