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## Solve quadratic equation by factoring method

Question

Solve the equation 2(x^{2} - 1) - 3(x + 1) = 0 by the factoring method.

Solution

- 2(x
^{2}- 1) - 3(x + 1) = 0 - using the perfect square formula, x
^{2}- a^{2}= (x + a) (x -a), so, x^{2}- 1 = (x + 1) (x - 1) - 2(x + 1) (x - 1) - 3(x + 1) = 0
- note: (x + 1) is a common factor
- (x + 1) [2(x - 1) - 3] = 0
- (x + 1) (2x - 2 - 3) = 0
- (x + 1) (2x - 5) = 0
- so, x + 1 = 0 or 2x - 5 = 0
- if x + 1 = 0, then x = -1
- if 2x - 5 = 0, then x = 5/2
- so, we get x
_{1}= -1 and x_{2}= 5/2

Substitute x_{1} = -1 into the original equation to verify if the left side of the equation is equal to the right side of the equation. If yes, then the value of
x_{1} = -1 is the solution of the original equation. Substitute x_{2} = 5/2 into the original equation to verify if the left side of the equation is equal to the
right side of the equation. If yes, then the value of x_{2} = 5/2 is the solution of the original equation. After testing we find that the value of x_{1} and
x_{2} are the solutions of the original equation.