SOLUTION: 2(x-4)^2+x^2=x(x+50)-46x solve the equation

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Question 337494: 2(x-4)^2+x^2=x(x+50)-46x solve the equation
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2%28x-4%29%5E2%2Bx%5E2=x%28x%2B50%29-46x Start with the given equation.


2%28x%5E2-8x%2B16%29%2Bx%5E2=x%28x%2B50%29-46x FOIL.


2x%5E2-16x%2B32%2Bx%5E2=x%5E2%2B50x-46x Distribute.


2x%5E2-16x%2B32%2Bx%5E2-1x%5E2-50x%2B46x=0 Get every term to the left side.


2x%5E2-20x%2B32=0 Combine like terms.


Notice that the quadratic 2x%5E2-20x%2B32 is in the form of Ax%5E2%2BBx%2BC where A=2, B=-20, and C=32


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-%28-20%29+%2B-+sqrt%28+%28-20%29%5E2-4%282%29%2832%29+%29%29%2F%282%282%29%29 Plug in A=2, B=-20, and C=32


x+=+%2820+%2B-+sqrt%28+%28-20%29%5E2-4%282%29%2832%29+%29%29%2F%282%282%29%29 Negate -20 to get 20.


x+=+%2820+%2B-+sqrt%28+400-4%282%29%2832%29+%29%29%2F%282%282%29%29 Square -20 to get 400.


x+=+%2820+%2B-+sqrt%28+400-256+%29%29%2F%282%282%29%29 Multiply 4%282%29%2832%29 to get 256


x+=+%2820+%2B-+sqrt%28+144+%29%29%2F%282%282%29%29 Subtract 256 from 400 to get 144


x+=+%2820+%2B-+sqrt%28+144+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%2820+%2B-+12%29%2F%284%29 Take the square root of 144 to get 12.


x+=+%2820+%2B+12%29%2F%284%29 or x+=+%2820+-+12%29%2F%284%29 Break up the expression.


x+=+%2832%29%2F%284%29 or x+=++%288%29%2F%284%29 Combine like terms.


x+=+8 or x+=+2 Simplify.


So the solutions are x+=+8 or x+=+2


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website.

Jim