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

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) (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 (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=88 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 8.69041575982343, -0.69041575982343. Here's your graph:

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