Question 67257
{{{x^2 - x = 3/4}}}
take 1/2 of the coefficient of x, square it, and add it to both sides
{{{x^2 - x + (1/4) = 1}}}
{{{(x - (1/2))^2 = 1}}}
{{{x - (1/2) = +1}}}
{{{x - (1/2) = -1}}}
{{{x = 3/2}}}
{{{x = -(1/2)}}}
check
{{{x^2 - x = 3/4}}}
{{{(3/2)^2 - (3/2) = 3/4}}}
{{{(9/4) - (6/4) = 3/4}}}
{{{3/4 = 3/4}}}
{{{(-1/2)^2 -(-1/2) = 3/4}}}
{{{(1/4) + (2/4) = 3/4}}}
{{{3/4 = 3/4}}}
OK
{{{2x^2 - 9x - 5 = 0}}}
{{{x^2 - (9/2)x = 5}}}
{{{x^2 - (9/2)x + (81/16) = (80/16) + (81/16)}}}
{{{x^2 - (9/2)x + (81/16) = 161/16}}}
{{{(x - 9/4)^2 = (161/16)}}}
{{{x - (9/4) = (+sqrt(161) / 4)}}}
{{{x - (9/4) = (-sqrt(161) / 4)}}}
{{{x = (9 + sqrt(161)) / 4}}}
{{{x = (9 - sqrt(161)) / 4}}}
check
{{{2x^2 - 9x - 5 = 0}}}
{{{2((9 + sqrt(161)) / 4)^2 - 9((9 + sqrt(161)) / 4) - 5 = 0}}}
this is really hard for me to check
I possibly made a mistake, but you get the idea