Question

Solve -2x^2 - 16x - 44 = 0

Answer 1

x = -4 + i√6 and

x = -4 - i√6

Explanation:

Divide all four terms by 2 to reduce the equation: -x^2 - 8x - 22 = 0.

Change all four signs: x^2 + 8x + 22

Complete the square of x^2 + 8x:

x^2 + 8x => x^2 + 8x + 16 - 16

Then our x^2 + 8x + 22 from above becomes x^2 + 8x + 16 + 22 - 16, or

(x + 4)^2 + 6 = 0, or (x + 4)^2 = -6

Taking the square root of both sides, we obtain:

x + 4 = ±√-6, or x + 4 = ±i√6

Solving for x, we get x = -4 ±i√6, and so the roots are:

x = -4 + i√6 and

x = -4 - i√6

Answer 2

Let's find the discriminant to see if there are any solutions at all. When ax² + bx + c = 0 the discriminant (D) is b² - 4ac. In our case, a = -2, b = -16 and c = -44 so D = (-16)² - 4(-2)(-44) = -96 which is less than 0. Since D < 0 the answer is no real solutions or x ∉ R.