Question 89373
{{{4x^2 + 2x - 3 = 0}}}
First, divide both sides by 4
{{{x^2 + (1/2)x - 3/4 = 0}}}
Add 3/4 to both sides
{{{x^2 + (1/2)x = 3/4}}}
Now, take 1/2 of the coefficient of x, square it, add it to both sides
{{{(1/2)/2 = 1/4}}} and {{{(1/4)^2 = 1/16}}}
{{{x^2 + (1/2)x + 1/16 = 3/4 + 1/16}}}
{{{(x + 1/4)^2 = 12/16 + 1/16}}}
{{{(x + 1/4)^2 = 13/16}}}
Take the square root of both sides
{{{x + 1/4 = sqrt(13) / 4}}}
{{{x = sqrt(13)/4 - 1/4}}}
{{{x = (sqrt(13) - 1)/4}}}
answer
You can check this by subbing it back into original
equation for x