Answer:
x = 5/2 + sqrt(61)/2 or x = 5/2 - sqrt(61)/2
Explanation:
Solve for x over the real numbers:
x^2 - 5 x - 6 = 3
Hint: | Solve the quadratic equation by completing the square.
Add 6 to both sides:
x^2 - 5 x = 9
Hint: | Take one half of the coefficient of x and square it, then add it to both sides.
Add 25/4 to both sides:
x^2 - 5 x + 25/4 = 61/4
Hint: | Factor the left hand side.
Write the left hand side as a square:
(x - 5/2)^2 = 61/4
Hint: | Eliminate the exponent on the left hand side.
Take the square root of both sides:
x - 5/2 = sqrt(61)/2 or x - 5/2 = -sqrt(61)/2
Hint: | Look at the first equation: Solve for x.
Add 5/2 to both sides:
x = 5/2 + sqrt(61)/2 or x - 5/2 = -sqrt(61)/2
Hint: | Look at the second equation: Solve for x.
Add 5/2 to both sides:
Answer: x = 5/2 + sqrt(61)/2 or x = 5/2 - sqrt(61)/2