Solve 5x2 = −30x − 65. x = −3 ± 2i x = −3 ± 4i x = −6 ± 2i x = −6 ± 4i
Accepted Solution
A:
Answer:x = -3 + 2 i or x = -3 - 2 iStep-by-step explanation:Solve for x:
5 x^2 = -5 (6 x + 13)
Expand out terms of the right hand side:
5 x^2 = -30 x - 65
Add 30 x + 65 to both sides:
5 x^2 + 30 x + 65 = 0
Divide both sides by 5:
x^2 + 6 x + 13 = 0
Subtract 13 from both sides:
x^2 + 6 x = -13
Add 9 to both sides:
x^2 + 6 x + 9 = -4
Write the left hand side as a square:
(x + 3)^2 = -4
Take the square root of both sides:
x + 3 = 2 i or x + 3 = -2 i
Subtract 3 from both sides:
x = -3 + 2 i or x + 3 = -2 i
Subtract 3 from both sides:
Answer: x = -3 + 2 i or x = -3 - 2 i