Solve the equation by using quadratic formula X^2+8x=5

x = sqrt (21) - 4 or x = - sqrt (21) - 4

Step-by-step explanation by using the quadratic formula:

Solve for x:

x^2 + 8 x = 5

Hint: | Move everything to the left hand side.

Subtract 5 from both sides:

x^2 + 8 x - 5 = 0

Hint: | Using the quadratic formula, solve for x.

x = (-8 ± sqrt (8^2 - 4 (-5))) / 2 = (-8 ± sqrt (64 + 20)) / 2 = (-8 ± sqrt (84)) / 2:

x = (-8 + sqrt (84)) / 2 or x = (-8 - sqrt (84)) / 2

Hint: | Simplify radicals.

sqrt (84) = sqrt (4*3*7) = sqrt (2^2*3*7) = 2sqrt (3*7) = 2 sqrt (21):

x = (2 sqrt (21) - 8) / 2 or x = (-2 sqrt (21) - 8) / 2

Hint: | Factor the greatest common divisor (gcd) of - 8, 2 sqrt (21) and 2 from - 8 + 2 sqrt (21).

Factor 2 from - 8 + 2 sqrt (21) giving 2 (sqrt (21) - 4):

x = 1/22 (sqrt (21) - 4) or x = (-2 sqrt (21) - 8) / 2

Hint: | Cancel common terms in the numerator and denominator.

(2 (sqrt (21) - 4)) / 2 = sqrt (21) - 4:

x = sqrt (21) - 4 or x = (-2 sqrt (21) - 8) / 2

Hint: | Factor the greatest common divisor (gcd) of - 8, - 2 sqrt (21) and 2 from - 8 - 2 sqrt (21).

Factor 2 from - 8 - 2 sqrt (21) giving 2 (-sqrt (21) - 4):

x = sqrt (21) - 4 or x = 1/22 (-sqrt (21) - 4)

Hint: | Cancel common terms in the numerator and denominator.

(2 (-sqrt (21) - 4)) / 2 = - sqrt (21) - 4:

Answer: x = sqrt (21) - 4 or x = - sqrt (21) - 4