Question

Solve for x. Write both solutions, separated by a
comma
2x^2 + 3x -- 9 = 0

Answer 1

x = - 3, x =
`(3)/(2)`

Explanation:

Given

2x² + 3x - 9 = 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 × - 9 = - 18 and sum = + 3

The factors are + 6 and - 3

Use these factors to split the x- term

2x² + 6x - 3x - 9 = 0 ( factor the first/second and third/fourth terms )

2x(x + 3) - 3(x + 3) = 0 ← factor out (x + 3) from each term

(x + 3)(2x - 3) = 0

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

2x - 3 = 0 ⇒ 2x = 3 ⇒ x =
`(3)/(2)`

Answer 2

Answer:3/2 or -3

Explanation:

2x2+3x-9=0

Factorise

Factors of -18 that can give +3 is +6&-3

Substitute

2x2+6x-3x-9=0

2x(x+3)-3(x+3)=0

(2x-3)(x+3)=0

2x-3=0

2x=3

X=3/2 or

X+3=0

X= -3

Answer is x=3/2 or -3