Question

Solve 5x2 = −30x − 65. x = −3 ± 2i x = −3 ± 4i x = −6 ± 2i x = −6 ± 4i

Answer 1

x= -3+or- 2i

Explanation:

Answer 2

x = -3 + 2 i or x = -3 - 2 i

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