Answer:
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
