Use the quadratic formula to solve the following quadratic equation:
`x^{2}-2x-20=4`
To solve the quadratic equation `x^2 - 2x - 20 = 4` using the quadratic formula, we first need to rewrite the equation in the standard form: `ax^2 + bx + c = 0`.
So, let's subtract 4 from both sides to get:
`x^2 - 2x - 24 = 0`
Now we have `a = 1`, `b = -2`, and `c = -24`.
The quadratic formula is given by:
`x = (-b ± sqrt(b^2 - 4ac)) / 2a`
Substituting the values for a, b, and c into the formula:
`x = (-(-2) ± sqrt((-2)^2 - 4(1)(-24))) / (2(1))`
Simplifying:
`x = (2 ± sqrt(4 + 96)) / 2`
`x = (2 ± sqrt(100)) / 2`
`x = (2 ± 10) / 2`
Now we have two possible solutions:
`x = (2 + 10) / 2` and `x = (2 - 10) / 2`
Simplifying further:
For `x = (2 + 10) / 2`:
`x = 12 / 2 = 6`
For `x = (2 - 10) / 2`:
`x = -8 / 2 = -4`
Therefore, the solutions to the quadratic equation `x^2 - 2x - 20 = 4` are `x = 6` and `x = -4`.