Solve the following quadratic equation by completing the square. If your solution has a radical then keep this in your answer and do not convert to a decimal.
x^2 - 2x - 35 = 0
To solve the quadratic equation x^2 - 2x - 35 = 0 by completing the square, we first rewrite the equation by moving the constant term to the other side:
x^2 - 2x = 35
Next, we need to complete the square for the quadratic term x^2 - 2x. To do this, we take half of the coefficient of x (-2) and square it:
(-2/2)^2 = (-1)^2 = 1
Add this result to both sides of the equation:
x^2 - 2x + 1 = 35 + 1
(x - 1)^2 = 36
Now, we can square root both sides to solve for x:
x - 1 = ±6
x = 1 ± 6
Thus, the solutions to the quadratic equation x^2 - 2x - 35 = 0 are x = 1 + 6 and x = 1 - 6 which simplifies to x = 7 and x = -5.