Question 110341
{{{4x^2 + 2x - 3 = 0}}}
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, and add to both sides
{{{x^2 + (1/2)x + (1/16) = (3/4) + (1/16)}}}
{{{x^2 + (1/2)x + (1/16) = 13/16}}}
{{{(x + (1/4))^2 = 13/16}}}
take the square root of both sides
{{{x + (1/4) = + sqrt(13/16)}}}
{{{x + (1/4) = - sqrt(13/16)}}} both of these are true
solve for x
{{{x = -(1/4) + (sqrt(13))/4}}}
{{{x = (-1 + sqrt(13)) / 4}}} answer
and
{{{x = -(1/4) - (sqrt(13))/4}}}
{{{x = (-1 - sqrt(13)) / 4}}} answer
You can check answers by plugging both (one at a time) into
the original equation. I checked one of them & checked OK