Solve quadratic equation by the completing square method

Question

Solve the equation x² - 6x - 72 = 0 by the completing square method

Solution

x² - 6x - 72 = 0

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

x² - 6x + (6/2)² - (6/2)² - 72 = 0

x² - 6x + 3² - 3² - 72 = 0

x² - 6x + 3² - 9 - 72 = 0

x² - 6x + 3² - 81 = 0

x² - 6x + 3² = 81

(x - 3)² = 9²

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 x₁ = 12 and x₂ = -6

Substitute x₁ = 12 and x₂ = -6 into the original equation, find that the left side of the equation is equal to the right side of the equation. So, x₁ = 12 and x₂ = -6 are the solutions of original equation.