Question 184959
Solve:
{{{x^2+6x-25 = 0}}} You can always solve a quadratic equation by:
a) The quadratic formula {{{x = (-b+-sqrt(b^2-4ac))/2a}}} or
b) Completing the square.
Let's use the "completing-the-square" method.
{{{x^2+6x-25 = 0}}} Add 25 to both sides.
{{{x^2+6x = 25}}} Now complete the square in x by adding the square of half the x-coefficient ({{{(6/2)^2 = 9}}}) to both sides of the equation.
{{{x^2+6x+9 = 25+9}}} Factor the left side and simplify the right side.
{{{(x+3)^2 = 34}}} Now take the square root of both sides.
{{{x+3 = 0+-sqrt(34)}}} Finally, subtract 3 from both sides.
{{{highlight(x = -3+-sqrt(34))}}}