Answer:
x = - 6, x =
Explanation:
set w(x) = g(x) , that is
2x² + 6x - 5 = - 3x² - 20x + 19 ( add 3x² to both sides )
5x² + 6x - 5 = - 20x + 19 ( add 20x to both sides )
5x² + 26x - 5 = 19 ( subtract 19 from both sides )
5x² + 26x - 24 = 0 ← in standard form
to factorise the expression
consider 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 × - 24 = - 120 and sum = + 26
the factors are + 30 and - 4
use these factors to split the x- term
5x² + 30x - 4x - 24 = 0 ( factor the first/second and third/fourth terms )
5x(x + 6) - 4(x + 6) = 0 ← factor out (x + 6) from each term
(x + 6)(5x - 4) = 0 ← in factored form
equate each factor to zero and solve for x
x + 6 = 0 ⇒ x = - 6
5x - 4 = 0 ⇒ 5x = 4 ⇒ x =