Answer:
x = - 6, x = [tex]\frac{3}{2}[/tex]
Step-by-step 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 = [tex]\frac{3}{2}[/tex]
