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.