Question

which are the solutions of the quadratic equation?
x² = -5x - 3
-5, 0
5, 0
\frac{-5 - \sqrt{13}}{2}, \frac{-5 + \sqrt{13}}{2}

Explanation:

Step1: Rearrange to standard form

$x^2 + 5x + 3 = 0$

Step2: Identify coefficients

For $ax^2+bx+c=0$, $a=1$, $b=5$, $c=3$

Step3: Apply quadratic formula

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Step4: Substitute values

$x=\frac{-5\pm\sqrt{5^2-4(1)(3)}}{2(1)}=\frac{-5\pm\sqrt{25-12}}{2}=\frac{-5\pm\sqrt{13}}{2}$

Answer:

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