Question 43454
Solve by factoring:
{{{2x^2 = 19x + 33}}} Rewrite in standard form.
{{{2x^2 - 19x - 33 = 0}}}

The factors will be in the form: (2x+a)(x+b)

Look at the first term {{{2x^2}}} and determine that the obvious factors are:
{{{(2x)(x) = 2x^2}}}

Now look at the last (constant) term and determine the factors (a and b) of -33. 
The choices are:
(a)(b)
(-1)(33) = -33
(1)(-33) = -33
(3)(-11) = -33
(-3)(11) = -33

Choose the pair from the above list such that: 2b+a = -19 which is the coefficient of the middle term of the rewritten quadratic equation.
The obvious choice is: a = 3 and b = -11 since 2(-11) + 3 = -22 + 3 = -19

Now you can write the factors of your quadratic equation:

{{{2x^2-19x-33 = (2x+3)(x-11)}}} Now you can solve the quadratic equation.

{{{(2x+3)(x-11) = 0}}} Apply the zero products principle.
{{{2x+3 = 0}}} and/or {{{x-11 = 0}}}
If {{{2x+3 = 0}}} then {{{2x = -3}}} and {{{x = -3/2}}}
If {{{x-11 = 0}}} then {{{x = 11}}}

The roots are:
{{{x = -3/2}}}
{{{x = 11}}}