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.