Question 102737
Solve this equation (this is not an expression!) by completing the square:
{{{x^2+5x = 2}}} Add the square of half the x-coefficient to both sides. This would be {{{(5/2)^2 = 25/4}}}
{{{x^2+5x+highlight(25/4) = 2+highlight(25/4)}}}Simplify.
{{{x^2+5x+25/4 = (8+25)/4}}}
{{{x^2+5x+25/4 = 33/4}}} Now factor the left side.
{{{(x+5/2)(x+5/2) = 33/4}}} Rewrite this as:
Ooops! I clicked the wrong button before finishing.
{{{(x+5/2)^2 = 33/4}}} Now take the square root of both sides.
{{{sqrt((x+5/2)^2) = sqrt(33/4)}}} Simplify.
{{{x+5/2 = sqrt(33)/2}}} or {{{x+5/2 = -sqrt(33)/2}}} Finally, subtract {{{5/2}}} from both sides of each solution.
{{{x = sqrt(33/2)-5/2}}} or {{{x = -sqrt(33)/2-5/2}}} The can be written:
{{{x = -((5-sqrt(33))/2)}}} or {{{x = -((5+sqrt(33))/2)}}}