Then solve the equation: x2−2x − 35 = 0 for x.

Answer 1

To solve the quadratic equation x^2 - 2x - 35 = 0 for x, we can use the quadratic formula which is given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

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

Substituting these values into the quadratic formula:

x = (-(-2) ± √((-2)^2 - 4(1)(-35))) / (2(1))

Simplifying further:

x = (2 ± √(4 + 140)) / 2

x = (2 ± √144) / 2

x = (2 ± 12) / 2

Thus, we have two possible solutions:

x₁ = (2 + 12) / 2 = 14 / 2 = 7

x₂ = (2 - 12) / 2 = -10 / 2 = -5

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