Question

solve the equation in the complex number system.
$x^2 - 10x + 50 = 0$
the solution set is {}. (use a comma to separate answers as needed

Explanation:

Step1: Identify quadratic coefficients

For $ax^2+bx+c=0$, here $a=1$, $b=-10$, $c=50$.

Step2: Calculate discriminant

$\Delta = b^2-4ac = (-10)^2 - 4(1)(50) = 100 - 200 = -100$

Step3: Apply quadratic formula

$x = \frac{-b \pm \sqrt{\Delta}}{2a} = \frac{10 \pm \sqrt{-100}}{2}$

Step4: Simplify complex root

$\sqrt{-100} = 10i$, so $x = \frac{10 \pm 10i}{2}$

Step5: Simplify the expression

$x = 5 \pm 5i$

Answer:

$\{5+5i, 5-5i\}$