Answer:
x = - [tex]\frac{2}{5}[/tex] , x = 4
Step-by-step explanation:
(2x + 3)² = (3x - 1)² ← expand both sides using FOIL
4x² + 12x + 9 = 9x² - 6x + 1 ( subtract 4x² + 12x + 9 from both sides )
0 = 5x² - 18x - 8
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 = 5 × - 8 = - 40 and sum = - 18
The factors are - 20 and + 2
Use these factors to split the x- term , then
5x² - 20x + 2x - 8 = 0 ( factor the first/second and third/fourth terms )
5x(x - 4) + 2(x - 4) = 0 ← factor out (x - 4) from each term
(x - 4)(5x + 2) = 0
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
5x + 2 = 0 ⇒ 5x = - 2 ⇒ x = - [tex]\frac{2}{5}[/tex]
