Question

using the quadratic formula to solve $x^2 + 20 = 2x$, what are the values of $x$?
$\bigcirc\\ 1\pm \sqrt{21}i$
$\bigcirc\\ -1\pm \sqrt{19}i$
$\bigcirc\\ 1\pm 2\sqrt{19}i$
$\bigcirc\\ 1\pm \sqrt{19}i$

Explanation:

Step1: Rearrange to standard form

$x^2 - 2x + 20 = 0$

Step2: Identify a, b, c

$a=1,\ b=-2,\ c=20$

Step3: Compute discriminant

$\Delta = b^2 - 4ac = (-2)^2 - 4(1)(20) = 4 - 80 = -76$

Step4: Apply quadratic formula

$x = \frac{-b \pm \sqrt{\Delta}}{2a} = \frac{2 \pm \sqrt{-76}}{2}$

Step5: Simplify the expression

$x = \frac{2 \pm 2\sqrt{19}i}{2} = 1 \pm \sqrt{19}i$

Answer:

$1\pm\sqrt{19}i$ (corresponding to the last option: $1\pm\sqrt{19}i$)