Evaluate the discriminant for the equation. Determine the number of real solutions.
x^2 - 6x = -9
To evaluate the discriminant for the equation, we need to use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation x^2 - 6x = -9, we have a = 1, b = -6, and c = 9.
Plugging these values into the quadratic formula:
x = (-(-6) ± √((-6)^2 - 4(1)(9))) / (2(1))
= (6 ± √(36 - 36)) / 2
= (6 ± √0) / 2
Since the discriminant is inside the square root, we can see that it is equal to 0.
Therefore, the equation has only one real solution.