Solve the quadratic equation. Please show your work.
x^2 - 9x - 17 = 0
To solve the quadratic equation x^2 - 9x - 17 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a is the coefficient of x^2, b is the coefficient of x, and c is the constant term.
For our equation, a = 1, b = -9, and c = -17.
Plugging these values into the quadratic formula, we get:
x = (-(-9) ± √((-9)^2 - 4(1)(-17))) / (2(1))
Simplifying further:
x = (9 ± √(81 + 68)) / 2
x = (9 ± √149) / 2
Now we have two solutions:
x = (9 + √149) / 2
x = (9 - √149) / 2
Both of these expressions are solutions to the quadratic equation x^2 - 9x - 17 = 0.