Answer:
x =
, x = - 2
Explanation:
Given
2x² + 3x = 2 ( subtract 2 from both sides )
2x² + 3x - 2 = 0
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 2 × - 2 = 4 and sum = + 3
The factors are + 4 and - 1
Use these factors to split the x- term
2x² + 4x - x - 2 = 0 ( factor the first/second and third/fourth terms )
2x(x + 2) - 1(x + 2) = 0 ← factor out (x + 2) from each term
(x + 2)(2x - 1) = 0
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
2x - 1 = 0 ⇒ 2x = 1 ⇒ x =