23x-256=x^2

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Solution for 23x-256=x^2 equation:


Simplifying
23x + -256 = x2

Reorder the terms:
-256 + 23x = x2

Solving
-256 + 23x = x2

Solving for variable 'x'.

Combine like terms: x2 + -1x2 = 0
-256 + 23x + -1x2 = 0

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

Divide each side by '-1'.
256 + -23x + x2 = 0

Move the constant term to the right:

Add '-256' to each side of the equation.
256 + -23x + -256 + x2 = 0 + -256

Reorder the terms:
256 + -256 + -23x + x2 = 0 + -256

Combine like terms: 256 + -256 = 0
0 + -23x + x2 = 0 + -256
-23x + x2 = 0 + -256

Combine like terms: 0 + -256 = -256
-23x + x2 = -256

The x term is -23x.  Take half its coefficient (-11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
-23x + 132.25 + x2 = -256 + 132.25

Reorder the terms:
132.25 + -23x + x2 = -256 + 132.25

Combine like terms: -256 + 132.25 = -123.75
132.25 + -23x + x2 = -123.75

Factor a perfect square on the left side:
(x + -11.5)(x + -11.5) = -123.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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