Answer:
x = 6 + 3 sqrt(21/5) or x = 6 - 3 sqrt(21/5)
Step-by-step explanation:
Solve for x over the real numbers:
(x - 12) (x + 4 x) = 9
(x - 12) (x + 4 x) = 5 x (x - 12):
5 x (x - 12) = 9
Divide both sides by 5:
x (x - 12) = 9/5
Expand out terms of the left hand side:
x^2 - 12 x = 9/5
Add 36 to both sides:
x^2 - 12 x + 36 = 189/5
Write the left hand side as a square:
(x - 6)^2 = 189/5
Take the square root of both sides:
x - 6 = 3 sqrt(21/5) or x - 6 = -3 sqrt(21/5)
Add 6 to both sides:
x = 6 + 3 sqrt(21/5) or x - 6 = -3 sqrt(21/5)
Add 6 to both sides:
Answer: x = 6 + 3 sqrt(21/5) or x = 6 - 3 sqrt(21/5)
