How do you solve x^2+20x+104=0x2+20x+104=0 by completing the square?

1 Answer
Aug 13, 2016

x = -10 +- 2ix=10±2i

Explanation:

Move the constant term to the RHS.

x^2 + 20x = -104x2+20x=104

Add the square of half the coefficient of the xx term to both sides:

x^2 + 20x + color(red)(10^2) = -104 + color(red)(10^2)x2+20x+102=104+102

This becomes:

(x+10)^2 = -104+100(x+10)2=104+100

(x+10)^2 = -4(x+10)2=4

Take square roots of both sides.

x+10 = +-sqrt(-4) = +-sqrt(4i^2) = +-2ix+10=±4=±4i2=±2i

x = -10 +- 2ix=10±2i