Question

which are the solutions of $x^2 = -11x + 4$?\
$\frac{-11 - \sqrt{137}}{2}$, $\frac{-11 + \sqrt{137}}{2}$\
$\frac{11 - \sqrt{137}}{2}$, $\frac{11 + \sqrt{137}}{2}$\
$\frac{11 - \sqrt{125}}{2}$, $\frac{11 + \sqrt{125}}{2}$

Explanation:

Step1: Rearrange to standard quadratic form

$x^2 + 11x - 4 = 0$

Step2: Identify coefficients for quadratic formula

For $ax^2+bx+c=0$, $a=1$, $b=11$, $c=-4$

Step3: Compute discriminant

$\Delta = b^2-4ac = 11^2 - 4(1)(-4) = 121 + 16 = 137$

Step4: Apply quadratic formula

$x = \frac{-b\pm\sqrt{\Delta}}{2a} = \frac{-11\pm\sqrt{137}}{2}$

Answer:

$\frac{-11-\sqrt{137}}{2}, \frac{-11+\sqrt{137}}{2}$