.5x+c(x-.5)=x(x-5)+10

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Solution for .5x+c(x-.5)=x(x-5)+10 equation: 


Simplifying
0.5x + c(x + -0.5) = x(x + -5) + 10

Reorder the terms:
0.5x + c(-0.5 + x) = x(x + -5) + 10
0.5x + (-0.5 * c + x * c) = x(x + -5) + 10
0.5x + (-0.5c + cx) = x(x + -5) + 10

Reorder the terms:
-0.5c + cx + 0.5x = x(x + -5) + 10

Reorder the terms:
-0.5c + cx + 0.5x = x(-5 + x) + 10
-0.5c + cx + 0.5x = (-5 * x + x * x) + 10
-0.5c + cx + 0.5x = (-5x + x2) + 10

Reorder the terms:
-0.5c + cx + 0.5x = 10 + -5x + x2

Solving
-0.5c + cx + 0.5x = 10 + -5x + x2

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Add '-0.5x' to each side of the equation.
-0.5c + cx + 0.5x + -0.5x = 10 + -5x + -0.5x + x2

Combine like terms: 0.5x + -0.5x = 0.0
-0.5c + cx + 0.0 = 10 + -5x + -0.5x + x2
-0.5c + cx = 10 + -5x + -0.5x + x2

Combine like terms: -5x + -0.5x = -5.5x
-0.5c + cx = 10 + -5.5x + x2

Reorder the terms:
-10 + -0.5c + cx + 5.5x + -1x2 = 10 + -5.5x + x2 + -10 + 5.5x + -1x2

Reorder the terms:
-10 + -0.5c + cx + 5.5x + -1x2 = 10 + -10 + -5.5x + 5.5x + x2 + -1x2

Combine like terms: 10 + -10 = 0
-10 + -0.5c + cx + 5.5x + -1x2 = 0 + -5.5x + 5.5x + x2 + -1x2
-10 + -0.5c + cx + 5.5x + -1x2 = -5.5x + 5.5x + x2 + -1x2

Combine like terms: -5.5x + 5.5x = 0.0
-10 + -0.5c + cx + 5.5x + -1x2 = 0.0 + x2 + -1x2
-10 + -0.5c + cx + 5.5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + -0.5c + cx + 5.5x + -1x2 = 0

The solution to this equation could not be determined.

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