Question 83493
Solve for x:
{{{x^2/2 - x/4 = 3/4}}} First, clear the fractions by multiplying through by 4 (the LCD).
{{{2x^2-x = 3}}} Now subtract 3 from both sides.
{{{2x^2-x-3 = 0}}} Next, factor the left side.
{{{(2x-3)(x+1) = 0}}} Apply the zero products principle.
{{{2x-3 = 0}}} and/or {{{x+1 = 0}}}
If {{{2x-3 = 0}}} then {{{2x = 3}}} and so {{{x = 3/2}}}
If {{{x+1 = 0}}} then {{{x = -1}}}
The solutions are:
{{{x = 3/2}}}
{{{x = -1}}}