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):

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