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Solve quadratic equation by factoring method

Question

Solve the equation 2(x2 - 1) - 3(x + 1) = 0 by the factoring method.

Solution

2(x2 - 1) - 3(x + 1) = 0
using the perfect square formula, x2 - a2 = (x + a) (x -a), so, x2 - 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 x1 = -1 and x2 = 5/2

Substitute x1 = -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 x1 = -1 is the solution of the original equation. Substitute x2 = 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 x2 = 5/2 is the solution of the original equation. After testing we find that the value of x1 and x2 are the solutions of the original equation.