Solve the quadratic equation. Please show your work x² - 9x - 17 = 0
To solve the quadratic equation, we can use the quadratic formula, which states that for any quadratic equation in the form of ax² + bx + c = 0, the solutions for x can be found using:
x = (-b ± √(b² - 4ac)) / (2a)
In the given quadratic equation x² - 9x - 17 = 0, we have:
a = 1, b = -9, and c = -17
Substituting these values into the quadratic formula, we get:
x = (-(-9) ± √((-9)² - 4(1)(-17))) / (2(1))
x = (9 ± √(81 + 68)) / 2
x = (9 ± √(149)) / 2
Therefore, the solutions to the quadratic equation x² - 9x - 17 = 0 are:
x = (9 + √149) / 2
x = (9 - √149) / 2