Question

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

Answer 1

`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=(-b-\sqrt\Delta)/(2a);\ x_2=(-b+\sqrt\Delta)/(2a)\\\\\sqrt\Delta=√(-12)=i√(12)=i√(4\cdot3)=i\sqrt4\cdot\sqrt3=2i\sqrt3`


`x_1=(-10-2i\sqrt3)/(2\cdot1)=-5-i\sqrt3\\\\x_2=(-10+2i\sqrt3)/(2\cdot1)=-5+i\sqrt3`

Answer 2

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