Question 209416
SOLVE BY COMPLETING THE SQUARE:
{{{4x^2-8x-2 = 0}}} First, divide both sides by 4 so as to get the {{{x^2}}} coefficient equal to 1.
{{{x^2-2x-1/2 = 0}}} Now add {{{1/2}}} to both sides.
{{{x^2-2x = 1/2}}} Complete the square in x by adding the square of half the x-coefficient to both sides, that's {{{(-2/2)^2 = 1}}}:
{{{x^2-2x+1 = (1/2)+1}}} Simplify.
{{{(x-1)^2 = 3/2}}} Take the square root of both sides.
{{{x-1 = sqrt(3/2)}}} or {{{x-1 = -sqrt(3/2)}}} Finally, add 1 to both sides of each solution.
{{{highlight(x = 1+sqrt(3/2))}}} or {{{highlight(x = 1-sqrt(3/2))}}}