SOLUTION: Help please! Let f(x) = x2 - 8x + 16. Find x so that f(x) = 22

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Help please! Let f(x) = x2 - 8x + 16. Find x so that f(x) = 22      Log On


   

Question 209614This question is from textbook
: Help please!
Let f(x) = x2 - 8x + 16. Find x so that f(x) = 22 This question is from textbook

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Let f(x) = x2 - 8x + 16. Find x so that f(x) = 22
.
Plug in the given value and solve for x:
22 = x^2 - 8x + 16
0 = x^2 - 8x - 6
Use the quadratic equation to solve for x. Doing so, yields:
x = {8.69, -0.69}
.
Details of quadratic follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-8x%2B-6+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-8%29%5E2-4%2A1%2A-6=88.

Discriminant d=88 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--8%2B-sqrt%28+88+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+88+%29%29%2F2%5C1+=+8.69041575982343
x%5B2%5D+=+%28-%28-8%29-sqrt%28+88+%29%29%2F2%5C1+=+-0.69041575982343

Quadratic expression 1x%5E2%2B-8x%2B-6 can be factored:
1x%5E2%2B-8x%2B-6+=+1%28x-8.69041575982343%29%2A%28x--0.69041575982343%29
Again, the answer is: 8.69041575982343, -0.69041575982343. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-8%2Ax%2B-6+%29