x2−2x − 35 = 0

Answer 1

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this equation, a = 1, b = -2, and c = -35.

Substituting these values into the quadratic formula, we get:

x = (-(-2) ± √((-2)² - 4(1)(-35))) / (2(1))
x = (2 ± √(4 + 140)) / 2
x = (2 ± √144) / 2
x = (2 ± 12) / 2

Now, we solve for both values of x:

For x = (2 + 12) / 2:
x = 14 / 2
x = 7

For x = (2 - 12) / 2:
x = -10 / 2
x = -5

Therefore, the solutions to the equation x² - 2x - 35 = 0 are x = 7 and x = -5.