Question

Which are the solutions of the quadratic equation x^2=-5x-3

Answer 1

The correct answer would be $\frac{-5 +/- \sqrt{13} }{2}$

In order to solve for this you must first get the equation equal to 0. 

x^2=-5x-3 ----> add 5x to both sides. 
x^2 + 5x = -3 ----> add 3 to both sides.
x^2 + 5x + 3 = 0

Now knowing this we can use the coefficients of each one in descending order of power as a, b and c. 

a = 1 (because it is the coefficient to x^2)
b = 5 (because it is the coefficient to x)
c = 3 (because it is the end number)

Now we can plug these values into the quadratic equation. 

$\frac{-b +/- \sqrt{b^{2} - 4ac } }{2a}$

$\frac{-5 +/- \sqrt{5^{2} - 4(3)(1) } }{2(1)}$

$\frac{-5 +/- \sqrt{13} }{2}$

And those would be your two answers.