Answer:
x=[tex]-\frac{3}{2},5[/tex]
Step-by-step explanation:
Factor and set each factor equal to zero.
Answer:
x = - [tex]\frac{3}{2}[/tex], x = 5
Step-by-step explanation:
Given
2x² - 7x - 9 = 6 ( subtract 6 from both sides )
2x² - 7x - 15 = 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 × - 15 = - 30 and sum = - 7
The factors are - 10 and + 3
Use these factors to split the x- term
2x² - 10x + 3x - 15 = 0 ( factor the first/second and third/fourth terms )
2x(x - 5) + 3(x - 5) = 0 ← factor out (x - 5) from each term
(x - 5)(2x + 3) = 0
Equate each factor to zero and solve for x
2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - [tex]\frac{3}{2}[/tex]
x - 5 = 0 ⇒ x = 5
