SOLUTION: x^2=20+8x 6x^2=5x+6 x^2+7=18

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Question 336173: x^2=20+8x
6x^2=5x+6
x^2+7=18
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one. Please only post one problem at a time.


x%5E2=20%2B8x Start with the given equation.


x%5E2-20-8x=0 Get every term to the left side.


x%5E2-8x-20=0 Rearrange the terms.


Notice that the quadratic x%5E2-8x-20 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-8, and C=-20


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-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2-4%281%29%28-20%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-8, and C=-20


x+=+%288+%2B-+sqrt%28+%28-8%29%5E2-4%281%29%28-20%29+%29%29%2F%282%281%29%29 Negate -8 to get 8.


x+=+%288+%2B-+sqrt%28+64-4%281%29%28-20%29+%29%29%2F%282%281%29%29 Square -8 to get 64.


x+=+%288+%2B-+sqrt%28+64--80+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-20%29 to get -80


x+=+%288+%2B-+sqrt%28+64%2B80+%29%29%2F%282%281%29%29 Rewrite sqrt%2864--80%29 as sqrt%2864%2B80%29


x+=+%288+%2B-+sqrt%28+144+%29%29%2F%282%281%29%29 Add 64 to 80 to get 144


x+=+%288+%2B-+sqrt%28+144+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%288+%2B-+12%29%2F%282%29 Take the square root of 144 to get 12.


x+=+%288+%2B+12%29%2F%282%29 or x+=+%288+-+12%29%2F%282%29 Break up the expression.


x+=+%2820%29%2F%282%29 or x+=++%28-4%29%2F%282%29 Combine like terms.


x+=+10 or x+=+-2 Simplify.


So the solutions are x+=+10 or x+=+-2

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

Also, feel free to check out my website.

Jim