Question

solve for x using the quadratic formula.
$x^2 - 8x + 20 = 0$
the solution set is
(type an exact answer, using radicals as needed. express complex numbers in terms of $i$. use a comma to separate answers as needed.)

Explanation:

Step1: Identify quadratic coefficients

For $ax^2+bx+c=0$, here $a=1$, $b=-8$, $c=20$

Step2: Recall quadratic formula

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

Step3: Calculate discriminant

$b^2-4ac=(-8)^2-4(1)(20)=64-80=-16$

Step4: Substitute into formula

$x=\frac{-(-8)\pm\sqrt{-16}}{2(1)}=\frac{8\pm4i}{2}$

Step5: Simplify the expression

$x=4\pm2i$

Answer:

$\{4+2i, 4-2i\}$