Solve -2x^2-16x-44 using quadratic formula

x = 4 + sqrt(38) or x = 4 - sqrt(38)

Step-by-step explanation using the quadratic formula:

Solve for x over the real numbers:

2 (x^2 - 8 x - 22) = 0

Divide both sides by 2:

x^2 - 8 x - 22 = 0

x = (8 ± sqrt((-8)^2 - 4 (-22)))/2 = (8 ± sqrt(64 + 88))/2 = (8 ± sqrt(152))/2:

x = (8 + sqrt(152))/2 or x = (8 - sqrt(152))/2

sqrt(152) = sqrt(8×19) = sqrt(2^3×19) = 2sqrt(2×19) = 2 sqrt(38):

x = (2 sqrt(38) + 8)/2 or x = (8 - 2 sqrt(38))/2

Factor 2 from 8 + 2 sqrt(38) giving 2 (sqrt(38) + 4):

x = 1/22 (sqrt(38) + 4) or x = (8 - 2 sqrt(38))/2

(2 (sqrt(38) + 4))/2 = sqrt(38) + 4:

x = sqrt(38) + 4 or x = (8 - 2 sqrt(38))/2

Factor 2 from 8 - 2 sqrt(38) giving 2 (4 - sqrt(38)):

x = 4 + sqrt(38) or x = 1/22 (4 - sqrt(38))

(2 (4 - sqrt(38)))/2 = 4 - sqrt(38):

 x = 4 + sqrt(38) or x = 4 - sqrt(38)