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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.