6.5-5x=x^2-10x+25

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Solution for 6.5-5x=x^2-10x+25 equation: 


Simplifying
6.5 + -5x = x2 + -10x + 25

Reorder the terms:
6.5 + -5x = 25 + -10x + x2

Solving
6.5 + -5x = 25 + -10x + x2

Solving for variable 'x'.

Reorder the terms:
6.5 + -25 + -5x + 10x + -1x2 = 25 + -10x + x2 + -25 + 10x + -1x2

Combine like terms: 6.5 + -25 = -18.5
-18.5 + -5x + 10x + -1x2 = 25 + -10x + x2 + -25 + 10x + -1x2

Combine like terms: -5x + 10x = 5x
-18.5 + 5x + -1x2 = 25 + -10x + x2 + -25 + 10x + -1x2

Reorder the terms:
-18.5 + 5x + -1x2 = 25 + -25 + -10x + 10x + x2 + -1x2

Combine like terms: 25 + -25 = 0
-18.5 + 5x + -1x2 = 0 + -10x + 10x + x2 + -1x2
-18.5 + 5x + -1x2 = -10x + 10x + x2 + -1x2

Combine like terms: -10x + 10x = 0
-18.5 + 5x + -1x2 = 0 + x2 + -1x2
-18.5 + 5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-18.5 + 5x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
18.5 + -5x + x2 = 0

Move the constant term to the right:

Add '-18.5' to each side of the equation.
18.5 + -5x + -18.5 + x2 = 0 + -18.5

Reorder the terms:
18.5 + -18.5 + -5x + x2 = 0 + -18.5

Combine like terms: 18.5 + -18.5 = 0.0
0.0 + -5x + x2 = 0 + -18.5
-5x + x2 = 0 + -18.5

Combine like terms: 0 + -18.5 = -18.5
-5x + x2 = -18.5

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -18.5 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -18.5 + 6.25

Combine like terms: -18.5 + 6.25 = -12.25
6.25 + -5x + x2 = -12.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = -12.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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