Answer:
x = - [tex]\frac{7}{2}[/tex], x = - 3
Step-by-step explanation:
Given
2x² + 13x = - 21 ( add 21 to both sides )
2x² + 13x + 21 = 0 ← in standard form
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term
product = 2 × 21 = 42 and sum = + 13
The factors are + 6 and + 7
Use these factors to split the x- term
2x² + 6x + 7x + 21 = 0 ( factor the first/second and third/fourth terms )
2x(x + 3) + 7(x + 3) = 0 ← factor out (x + 3) from each term
(x + 3)(2x + 7) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
2x + 7 = 0 ⇒ 2x = - 7 ⇒ x = - [tex]\frac{7}{2}[/tex]
