Then solve the equation: x2−2x − 35 = 0 for x.
Please show all of your work.
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(4 points)
To solve the equation x^2 - 2x - 35 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
where a = 1, b = -2, and c = -35.
Plugging these values into the 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
We have two cases to consider:
Case 1: x = (2 + 12) / 2 = 14 / 2 = 7
Case 2: x = (2 - 12) / 2 = -10 / 2 = -5
Therefore, the solutions to the equation x^2 - 2x - 35 = 0 are x = 7 and x = -5.