Question 358140
{{{x^2+18x-4=0}}}
This is a quadratic equation. After you get one side to be zero, you either factor the non-zero side or use the Quadratic Formula. Since we already have one side equal to zero and since the non-zero side cannot be factored easily, we will go straight to the Quadratic Formula, {{{x = (-b +- sqrt(b^2 -4ac))/(2a)}}}, where the "a", "b" and "c" are from {{{ax^2 + bx + c = 0}}}. Your a=1, b=18 and c =-4. So
{{{x = (-(18) +- sqrt((18)^2 - 4(1)(-4)))/(2(1))}}}
Simplifying:
{{{x = (-(18) +- sqrt(324 - 4(1)(-4)))/(2(1))}}}
{{{x = (-18 +- sqrt(324 + 16))/2}}}
{{{x = (-18 +- sqrt(340))/2}}}
{{{x = (-18 +- sqrt(4*85))/2}}}
{{{x = (-18 +- sqrt(4)*sqrt(85))/2}}}
{{{x = (-18 +- 2*sqrt(85))/2}}}
{{{x = (2(-9 +- sqrt(85)))/2}}}
{{{x = (cross(2)(-9 +- sqrt(85)))/cross(2)}}}
{{{x = -9 +- sqrt(85)}}}
In "long form" this is:
{{{x = -9 + sqrt(85)}}} or {{{x = -9 - sqrt(85)}}}