SOLUTION: Let f(x)=(x-2)^2.Find x such that f(x)=25

Question 224746: Let f(x)=(x-2)^2.Find x such that f(x)=25
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. Given

Step 2. Subtract 25 from the above equation to yield a quadratic as follows

Step 3. To 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 4. ANSWER: Solutions are 7 and -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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