Answer:
p = - 2, p = - [tex]\frac{21}{2}[/tex]
Step-by-step explanation:
Given
3p(2p - 1) - 17 = (2p - 5)² ← expand factors on both sides
6p² - 3p - 17 = 4p² - 20p + 25 ( subtract 4p² - 20p + 25 from both sides )
2p² + 17p - 42 = 0
Consider the factors of the product of the coefficient of the p² term and the constant term which sum to give the coefficient of the p- term.
product = 2 × - 42 = - 84 and sum = + 17
Factors are + 21 and - 4
Use these factors to split the p- term
2p² - 4p + 21p - 42 = 0 ( factor the first/second and third/fourth terms )
2p(p - 2) + 21(p - 2) = 0 ← factor out (p - 2) from each term
(p - 2)(2p + 21) = 0
Equate each factor to zero and solve for p
p - 2 = 0 ⇒ p = 2
2p + 21 = 0 ⇒ 2p = - 21 ⇒ p = - [tex]\frac{21}{2}[/tex]
