Question 220853
{{{4x^2 - 4x - 99 = 0}}}
First divide both sides by {{{4}}}
{{{x^2 - x - 99/4 = 0}}}
Now add {{{99/4}}} to both sides
{{{x^2 - x = 99/4}}}
Now take 1/2 of the coefficient of {{{x}}}
which is {{{-1}}}, square it, and add it to
both sides
{{{x^2 - x + (-1/2)^2 = 99/4 + (-1/2)^2}}}
{{{x^2 - x + 1/4 = 99/4 + 1/4}}}
{{{x^2 - x + 1/4 = 100/4}}}
Notice that both sides are perfect squares
{{{(x - 1/2)^2 = (10/2)^2}}}
I'll take the square root of both sides
{{{x - 1/2 = 10/2}}}
{{{x = 10/2 + 1/2}}}
{{{x = 11/2}}}
There is also a negative square root
{{{x - 1/2 = -10/2}}}
{{{x = -9/2}}}
The roots are {{{x = 11/2}}} and {{{x = -9/2}}}
I'll plot it to verify
{{{ graph( 600, 600, -10, 10, -110, 5, 4x^2 - 4x - 99) }}}
Looks about right