Solve quadratic equation by the completing square method

Question

Solve the equation x^{2} - 6x - 72 = 0 by the completing square method

Solution

x^{2} - 6x - 72 = 0

add and subtract the square of the half the coefficient of x-term

x^{2} - 6x + (6/2)^{2} - (6/2)^{2} - 72 = 0

x^{2} - 6x + 3^{2} - 3^{2} - 72 = 0

x^{2} - 6x + 3^{2} - 9 - 72 = 0

x^{2} - 6x + 3^{2} - 81 = 0

x^{2} - 6x + 3^{2} = 81

(x - 3)^{2} = 9^{2}

square both side of the equation

x - 3 = + - 9

so, we get two equations, one is x - 3 = 9 and other is x - 3 = -9

solve x - 3 = 9

x = 3 + 9

x = 12

solve x - 3 = -9

x = 3 - 9

x = -6

so, we get x_{1} = 12 and x_{2} = -6

Substitute x_{1} = 12 and x_{2} = -6 into the original equation, find that the left side of the equation is equal to the right side of the equation.
So, x_{1} = 12 and x_{2} = -6 are the solutions of original equation.