Complete the square to solve the following quadratic equation: x^2-6x-20=20
To complete the square, we want to rewrite the equation in the form: (x - h)^2 = k.
1. Move the constant term to the right side of the equation:
x^2 - 6x - 20 - 20 = 0
x^2 - 6x - 40 = 0
2. Take half of the coefficient of x (-6) and square it: (-6/2)^2 = 9.
3. Add this value inside the parentheses on the left side, and add it to the right side of the equation:
x^2 - 6x + 9 - 40 = 9
(x - 3)^2 - 40 = 9
4. Simplify the right side of the equation:
(x - 3)^2 - 40 = 9
(x - 3)^2 = 49
5. Take the square root of both sides, remembering to consider both positive and negative roots:
x - 3 = ±√49
x - 3 = ±7
6. Solve for x:
x = 3 + 7 = 10
or
x = 3 - 7 = -4
Thus, the quadratic equation x^2 - 6x - 20 = 20 has two solutions: x = 10 and x = -4.