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:

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

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