Expand the following:
(x + 2) (2 x + 5) = 11 (x + 2)
(x + 2) (2 x + 5) = (x) (2 x) + (x) (5) + (2) (2 x) + (2) (5) = 2 x^2 + 5 x + 4 x + 10 = 2 x^2 + 9 x + 10:
2 x^2 + 9 x + 10 = 11 (x + 2)
11 (x + 2) = 11 x + 11 2:
2 x^2 + 9 x + 10 = 11 x + 11 2
11×2 = 22:
2 x^2 + 9 x + 10 = 11 x + 22
Subtract 11 x + 22 from both sides of 2 x^2 + 9 x + 10 = 11 x + 22:
2 x^2 + 9 x - 11 x + 22 + 10 = (11 x + 22) - 11 x + 22
(11 x + 22) - (11 x + 22) = 0:
2 x^2 + 9 x - (11 x + 22) + 10 = 0
-(11 x + 22) = -22 - 11 x:
2 x^2 + 9 x + -22 - 11 x + 10 = 0
Grouping like terms, 2 x^2 + 9 x - 11 x - 22 + 10 = 2 x^2 + (9 x - 11 x) + (10 - 22):
2 x^2 + (9 x - 11 x) + (10 - 22) = 0
9 x - 11 x = -2 x:
2 x^2 + -2 x + (10 - 22) = 0
10 - 22 = -12:
Answer: |2 x^2 - 2 x + -12 = 0
