SOLUTION: Solve for X: 25x^2-80x=-64

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Question 317822: Solve for X:
25x^2-80x=-64
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

25x%5E2-80x=-64 Start with the given equation.


25x%5E2-80x%2B64=0 Add 64 to both sides.


Notice that the quadratic 25x%5E2-80x%2B64 is in the form of Ax%5E2%2BBx%2BC where A=25, B=-80, and C=64


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-%28-80%29+%2B-+sqrt%28+%28-80%29%5E2-4%2825%29%2864%29+%29%29%2F%282%2825%29%29 Plug in A=25, B=-80, and C=64


x+=+%2880+%2B-+sqrt%28+%28-80%29%5E2-4%2825%29%2864%29+%29%29%2F%282%2825%29%29 Negate -80 to get 80.


x+=+%2880+%2B-+sqrt%28+6400-4%2825%29%2864%29+%29%29%2F%282%2825%29%29 Square -80 to get 6400.


x+=+%2880+%2B-+sqrt%28+6400-6400+%29%29%2F%282%2825%29%29 Multiply 4%2825%29%2864%29 to get 6400


x+=+%2880+%2B-+sqrt%28+0+%29%29%2F%282%2825%29%29 Subtract 6400 from 6400 to get 0


x+=+%2880+%2B-+sqrt%28+0+%29%29%2F%2850%29 Multiply 2 and 25 to get 50.


x+=+%2880+%2B-+0%29%2F%2850%29 Take the square root of 0 to get 0.


x+=+%2880+%2B+0%29%2F%2850%29 or x+=+%2880+-+0%29%2F%2850%29 Break up the expression.


x+=+%2880%29%2F%2850%29 or x+=++%2880%29%2F%2850%29 Combine like terms.


x+=+8%2F5 or x+=+8%2F5 Simplify.


So the only solutions is x+=+8%2F5