Question

Which are the solutions of x2 = –13x – 4?

Answer 1

If you are using e2020 the answer is D. 

Answer 2

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

$x1=-0.315\\ x2=-12.685$