which are the solutions of $x^{2}=-5x + 8$?\n$\frac{-5-sqrt{57}}{2},\frac{-5+sqrt{57}}{2}$\n$\frac{-5-sqrt{7}…

Explanation:

Step1: Rearrange to standard quadratic form

$x^{2}+5x - 8=0$

Step2: Identify coefficients for quadratic formula

For $ax^{2}+bx + c = 0$, here $a = 1$, $b = 5$, $c=-8$.

Step3: Apply quadratic formula $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$

$x=\frac{-5\pm\sqrt{5^{2}-4\times1\times(-8)}}{2\times1}=\frac{-5\pm\sqrt{25 + 32}}{2}=\frac{-5\pm\sqrt{57}}{2}$

Answer:

$\frac{-5-\sqrt{57}}{2},\frac{-5+\sqrt{57}}{2}$