Question 216874
solve the equation by completing the square: 4x^2 + 40x + 280 = 0
4x^2 + 40x + ___ = -280
:
Divide both sides by 4
x^2 + 10x + ____ = -70
:
Find the value of the 3rd term that completes the square
using the coefficient of x: (10/2)^2 = 25
x^2 + 10x + 25 = -70 + 25
:
x^2 + 10x + 25 = -45
:
Which is:
(x + 5)^2 = -45
:
Find the square root of both sides
x + 5 = +/-{{{sqrt(-45)}}}
:
x + 5 = +/-{{{sqrt(9*-1*5)}}}
:
Extract the square root of -1 and 9
x + 5 = +/-{{{3i*sqrt(5)}}}
:
Two solutions
{{{x = -5 + 3i*sqrt(5)}}}
and
{{{x = -5 - 3i*sqrt(5)}}}