Answer:
q = - 5 , q =
Explanation:
5q² + 18q = 35 ( subtract 35 from both sides )
5q² + 18q - 35 = 0 ← in standard form
consider the factors of the product of the coefficient of the q² term and the constant term which sum to give the coefficient of the q- term
product = 5 × - 35 = - 175 and sum = + 18
the factors are + 25 and - 7
use these factors to split the q- term
5q² + 25q - 7q - 35 = 0 ( factor the first/second and third/fourth terms )
5q(q + 5) - 7(q + 5) = 0 ← factor out (q + 5) from each term
(q + 5)(5q - 7) = 0 ← in factored form
equate each factor to zero and solve for q
q + 5 = 0 ( subtract 5 from both sides )
q = - 5
5q - 7 = 0 ( add 7 to both sides )
5q = 7 ( divide both sides by 5 )
q =
solutions are q = - 5 , q =