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

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Question 224746: Let f(x)=(x-2)^2.Find x such that f(x)=25
Answer by drj(1380) About Me  (Show Source):
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Let f(x)=(x-2)^2.Find x such that f(x)=25

Step 1. Given f%28x%29=25=%28x-2%29%5E2=x%5E2-4x%2B4

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

x%5E2-4x%2B4-25=25-25

x%5E2-4x-21=0

Step 3. To solve, use the quadratic formula given as

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

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

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-4x%2B-21+=+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=%28-4%29%5E2-4%2A1%2A-21=100.

Discriminant d=100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+100+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+100+%29%29%2F2%5C1+=+7
x%5B2%5D+=+%28-%28-4%29-sqrt%28+100+%29%29%2F2%5C1+=+-3

Quadratic expression 1x%5E2%2B-4x%2B-21 can be factored:
1x%5E2%2B-4x%2B-21+=+1%28x-7%29%2A%28x--3%29
Again, the answer is: 7, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B-21+%29



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