(x-14)(x-14)+(7-x)(7-x)=x

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Solution for (x-14)(x-14)+(7-x)(7-x)=x equation: 


Simplifying
(x + -14)(x + -14) + (7 + -1x)(7 + -1x) = x

Reorder the terms:
(-14 + x)(x + -14) + (7 + -1x)(7 + -1x) = x

Reorder the terms:
(-14 + x)(-14 + x) + (7 + -1x)(7 + -1x) = x

Multiply (-14 + x) * (-14 + x)
(-14(-14 + x) + x(-14 + x)) + (7 + -1x)(7 + -1x) = x
((-14 * -14 + x * -14) + x(-14 + x)) + (7 + -1x)(7 + -1x) = x
((196 + -14x) + x(-14 + x)) + (7 + -1x)(7 + -1x) = x
(196 + -14x + (-14 * x + x * x)) + (7 + -1x)(7 + -1x) = x
(196 + -14x + (-14x + x2)) + (7 + -1x)(7 + -1x) = x

Combine like terms: -14x + -14x = -28x
(196 + -28x + x2) + (7 + -1x)(7 + -1x) = x

Multiply (7 + -1x) * (7 + -1x)
196 + -28x + x2 + (7(7 + -1x) + -1x * (7 + -1x)) = x
196 + -28x + x2 + ((7 * 7 + -1x * 7) + -1x * (7 + -1x)) = x
196 + -28x + x2 + ((49 + -7x) + -1x * (7 + -1x)) = x
196 + -28x + x2 + (49 + -7x + (7 * -1x + -1x * -1x)) = x
196 + -28x + x2 + (49 + -7x + (-7x + 1x2)) = x

Combine like terms: -7x + -7x = -14x
196 + -28x + x2 + (49 + -14x + 1x2) = x

Reorder the terms:
196 + 49 + -28x + -14x + x2 + 1x2 = x

Combine like terms: 196 + 49 = 245
245 + -28x + -14x + x2 + 1x2 = x

Combine like terms: -28x + -14x = -42x
245 + -42x + x2 + 1x2 = x

Combine like terms: x2 + 1x2 = 2x2
245 + -42x + 2x2 = x

Solving
245 + -42x + 2x2 = x

Solving for variable 'x'.

Reorder the terms:
245 + -42x + -1x + 2x2 = x + -1x

Combine like terms: -42x + -1x = -43x
245 + -43x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
245 + -43x + 2x2 = 0

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

Divide each side by '2'.
122.5 + -21.5x + x2 = 0

Move the constant term to the right:

Add '-122.5' to each side of the equation.
122.5 + -21.5x + -122.5 + x2 = 0 + -122.5

Reorder the terms:
122.5 + -122.5 + -21.5x + x2 = 0 + -122.5

Combine like terms: 122.5 + -122.5 = 0.0
0.0 + -21.5x + x2 = 0 + -122.5
-21.5x + x2 = 0 + -122.5

Combine like terms: 0 + -122.5 = -122.5
-21.5x + x2 = -122.5

The x term is -21.5x.  Take half its coefficient (-10.75).
Square it (115.5625) and add it to both sides.

Add '115.5625' to each side of the equation.
-21.5x + 115.5625 + x2 = -122.5 + 115.5625

Reorder the terms:
115.5625 + -21.5x + x2 = -122.5 + 115.5625

Combine like terms: -122.5 + 115.5625 = -6.9375
115.5625 + -21.5x + x2 = -6.9375

Factor a perfect square on the left side:
(x + -10.75)(x + -10.75) = -6.9375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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