Question

`2x^(2) + 9x - 18 = 0`
​

Answer 1

x = - 6, x =
`(3)/(2)`

Explanation:

Assuming you require the solution to the equation

Given

2x² + 9x - 18 = 0

To factor the quadratic

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 × - 18 = - 36 and sum = + 9

The factors are + 12 and - 3

Use these factors to split the x- term

2x² + 12x - 3x - 18 = 0 ( factor the first/second and third/fourth terms )

2x(x + 6) - 3(x + 6) = 0 ← factor out (x + 6) from each term

(x + 6)(2x - 3) = 0

Equate each factor to zero and solve for x

x + 6 = 0 ⇒ x = - 6

2x - 3 = 0 ⇒ 2x = 3 ⇒ x =
`(3)/(2)`