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 equation x^2 - 2x - 35 = 0 by completing the square, we follow these steps:
1. Move the constant term to the other side of the equation:
x^2 - 2x = 35
2. To complete the square, take half of the coefficient of x (-2), square it, and add it to both sides of the equation:
x^2 - 2x + (-2/2)^2 = 35 + (-2/2)^2
x^2 - 2x + 1 = 36
x^2 - 2x + 1 = (x - 1)^2
3. Rewrite the equation with the completed square term:
(x - 1)^2 = 36
4. Take the square root of both sides to solve for x:
x - 1 = ±√36
x - 1 = ±6
x = 1 ± 6
Therefore, the solutions to the equation x^2 - 2x - 35 = 0 are x = 1 + 6 = 7 and x = 1 - 6 = -5.