SOLUTION: Let f(x) = (x � 2)^2. Find x such that f(x) = 25 I do not understand the question :(

Question 224605: Let f(x) = (x � 2)^2. Find x such that f(x) = 25
I do not understand the question :(
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
Let f(x) = (x � 2)^2. Find x such that f(x) = 25

Step 1. So the equation becomes

Step 2. Multiply out the squared term:

Step 3. Subtract 25 from both sides of the equation: or

Step 4. Top solve, use the quadratic formula given as

where a=1, b=-4, and c=-21

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=100 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 7, -3. Here's your graph:

Step 5. Check solutions 7 and -3 with

which is a true statement.

which is another true statement.

Step 6. ANSWER: Solutions are x=7 and x=-3.

I hope the above steps and explanation were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV
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