Solve for x: 2x²+3x=2. Please use factoring. Thanks!

x = , x = - 2

Step-by-step 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 =

18

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