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

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

Step-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

x = - 3+or - 2i