[tex]x^2 + 2x = 24\\x^2+2x+1=25\\(x+1)^2=25\\x+1=5 \vee x+1=-5\\\x=4 \vee x=-6[/tex]
Answer:
x = - 6, x = 4
Step-by-step explanation:
Given
x² + 2x = 24 ( subtract 24 from both sides )
x² + 2x - 24 = 0
To factorise the quadratic
Consider the factors of the constant term (- 24) which sum to give the coefficient of the x- term (+ 2)
The factors are + 6 and - 4, since
6 × - 4 = - 24 and 6 - 4 = + 2, hence
(x + 6)(x - 4) = 0
Equate each factor to zero and solve for x
x + 6 = 0 ⇒ x = - 6
x - 4 = 0 ⇒ x = 4
