SOLUTION: 3(x-6)^2+x^2=x(x+72)-48x

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Question 215001: 3(x-6)^2+x^2=x(x+72)-48x
Found 2 solutions by jim_thompson5910, drj:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3%28x-6%29%5E2%2Bx%5E2=x%28x%2B72%29-48x Start with the given equation.


3%28x%5E2-12x%2B36%29%2Bx%5E2=x%28x%2B72%29-48x FOIL


3x%5E2-36x%2B108%2Bx%5E2=x%5E2%2B72x-48x Distribute


3x%5E2-36x%2B108%2Bx%5E2-1x%5E2-72x%2B48x=0 Get every term to the left side.


3x%5E2-60x%2B108=0 Combine like terms.


Notice that the quadratic 3x%5E2-60x%2B108 is in the form of Ax%5E2%2BBx%2BC where A=3, B=-60, and C=108


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-60%29+%2B-+sqrt%28+%28-60%29%5E2-4%283%29%28108%29+%29%29%2F%282%283%29%29 Plug in A=3, B=-60, and C=108


x+=+%2860+%2B-+sqrt%28+%28-60%29%5E2-4%283%29%28108%29+%29%29%2F%282%283%29%29 Negate -60 to get 60.


x+=+%2860+%2B-+sqrt%28+3600-4%283%29%28108%29+%29%29%2F%282%283%29%29 Square -60 to get 3600.


x+=+%2860+%2B-+sqrt%28+3600-1296+%29%29%2F%282%283%29%29 Multiply 4%283%29%28108%29 to get 1296


x+=+%2860+%2B-+sqrt%28+2304+%29%29%2F%282%283%29%29 Subtract 1296 from 3600 to get 2304


x+=+%2860+%2B-+sqrt%28+2304+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%2860+%2B-+48%29%2F%286%29 Take the square root of 2304 to get 48.


x+=+%2860+%2B+48%29%2F%286%29 or x+=+%2860+-+48%29%2F%286%29 Break up the expression.


x+=+%28108%29%2F%286%29 or x+=++%2812%29%2F%286%29 Combine like terms.


x+=+18 or x+=+2 Simplify.


So the solutions are x+=+18 or x+=+2

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
3%28x-6%29%5E2%2Bx%5E2=x%28x%2B72%29-48x

Step 1. Multiply and add to simplify equations

3%28x%5E2-12x%2B36%29%2Bx%5E2=x%5E2%2B72x-48x

3x%5E2-36x%2B108%2Bx%5E2=x%5E2%2B24x

Step 2. Subtract x%5E2%2B24x

3x%5E2-36x%2B108%2Bx%5E2-x%5E2-24x=x%5E2%2B24x-x%5E2-24

3x%5E2-60x%2B108=0

Step 3. Solve using the quadratic equation given below as

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-60x%2B108+=+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=%28-60%29%5E2-4%2A3%2A108=2304.

Discriminant d=2304 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--60%2B-sqrt%28+2304+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-60%29%2Bsqrt%28+2304+%29%29%2F2%5C3+=+18
x%5B2%5D+=+%28-%28-60%29-sqrt%28+2304+%29%29%2F2%5C3+=+2

Quadratic expression 3x%5E2%2B-60x%2B108 can be factored:
3x%5E2%2B-60x%2B108+=+3%28x-18%29%2A%28x-2%29
Again, the answer is: 18, 2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-60%2Ax%2B108+%29



Step 4. The solutions are 2 and 18.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J