Solve for x over the real numbers:
x^2 - 10 x - 27 = 0
Hint: | Solve the quadratic equation by completing the square.
Add 27 to both sides:
x^2 - 10 x = 27
Hint: | Take one half of the coefficient of x and square it, then add it to both sides.
Add 25 to both sides:
x^2 - 10 x + 25 = 52
Hint: | Factor the left hand side.
Write the left hand side as a square:
(x - 5)^2 = 52
Hint: | Eliminate the exponent on the left hand side.
Take the square root of both sides:
x - 5 = 2 sqrt(13) or x - 5 = -2 sqrt(13)
Hint: | Look at the first equation: Solve for x.
Add 5 to both sides:
x = 5 + 2 sqrt(13) or x - 5 = -2 sqrt(13)
Hint: | Look at the second equation: Solve for x.
Add 5 to both sides:
Answer:
x = 5 + 2√(13) or x = 5 - 2√(13)
