Question

Solve the equation: 2x^2 + 3x = 2

Answer 1

x = - 2, x =
`(1)/(2)`

Explanation:

Given

2x² + 3x = 2 ( subtract 2 from both sides )

2x² + 3x - 2 = 0

Consider the factors of the product of the coefficient 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 =
`(1)/(2)`

Answer 2

x = -2 or x = 1/2

Explanation:

First get the eq in standard form, which means:

x² should not have that 2 in front of it

move the other 2 to the left

so first let's divide by 2:

x² + 3/2 x = 1

now move the 1 to the left

x² + 3/2 x - 1 = 0

now look for two numbers that, when multiplied, give -1, and when added, give 3/2. This is a bit of trial-and-error if you want to solve in this way.

The numbers are 2 and -1/2, since 2*-1/2 = -1, and 2 - 1/2 = 3/2

The factorization thus is:

x² + 3/2 x - 1 = (x+2)(x-1/2) = 0

Either factor (x+2) or (x-1/2) can be zero to solve the solution, hence x = -2 or x = 1/2