Question

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

Answer 1

To solve the equation x^2 - 2x - 35 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

For 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))

Simplifying further:

x = (2 ± √(4 + 140)) / 2

x = (2 ± √(144)) / 2

x = (2 ± 12) / 2

Therefore, the two solutions for x are:

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

and

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

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