Use the quadratic formula to solve the following quadratic equation:
`x^{2}-2x-20=4`
Put your answer in the solution box below.
To solve the quadratic equation `x^{2}-2x-20=4` using the quadratic formula, we first need to rearrange the equation to have a zero on one side:
`x^{2}-2x-20-4 = 0`
Combining like terms:
`x^{2}-2x-24 = 0`
Now, we can apply the quadratic formula, which states that for an equation in the form ax^2 + bx + c = 0, the solutions for x can be found using:
`x = (-b+-sqrt(b^{2}-4ac))/(2a)`
For our equation with a=1, b=-2, and c=-24, the quadratic formula becomes:
`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 = 12/2 = 6`
and
`x = (2 - 10)/2 = -8/2 = -4`
So, the solutions to the given quadratic equation are x = 6 and x = -4.