Question

What is the solution to x2 + 10x + 28 = 0 when written in the form a ± bi?

Answer 1

use the quadratic formular:
x=[-10+√(10²-4*1*28)]/2*1 or x=[-10-√(10²-4*1*28)]/2*1
x=[-10+√(-12)]/2 or x=[-10-√(-12)]/2
x=-5+√3i or x=-5-√3i

Answer 2

$x^2+10x+28=0\\\\a=1;\ b=10;\ c=28\\\\\Delta=b^2-4ac\\\\\Delta=10^2-4\cdot1\cdot28=100-112=-112\\\\x_1=\dfrac{-b-\sqrt\Delta}{2a};\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt{-12}=i\sqrt{12}=i\sqrt{4\cdot3}=i\sqrt4\cdot\sqrt3=2i\sqrt3$

$x_1=\dfrac{-10-2i\sqrt3}{2\cdot1}=-5-i\sqrt3\\\\x_2=\dfrac{-10+2i\sqrt3}{2\cdot1}=-5+i\sqrt3$