(x)=x^2-6x+13

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Solution for (x)=x^2-6x+13 equation: 


Simplifying
(x) = x2 + -6x + 13
x = x2 + -6x + 13

Reorder the terms:
x = 13 + -6x + x2

Solving
x = 13 + -6x + x2

Solving for variable 'x'.

Reorder the terms:
-13 + x + 6x + -1x2 = 13 + -6x + x2 + -13 + 6x + -1x2

Combine like terms: x + 6x = 7x
-13 + 7x + -1x2 = 13 + -6x + x2 + -13 + 6x + -1x2

Reorder the terms:
-13 + 7x + -1x2 = 13 + -13 + -6x + 6x + x2 + -1x2

Combine like terms: 13 + -13 = 0
-13 + 7x + -1x2 = 0 + -6x + 6x + x2 + -1x2
-13 + 7x + -1x2 = -6x + 6x + x2 + -1x2

Combine like terms: -6x + 6x = 0
-13 + 7x + -1x2 = 0 + x2 + -1x2
-13 + 7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-13 + 7x + -1x2 = 0

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

Divide each side by '-1'.
13 + -7x + x2 = 0

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + -7x + -13 + x2 = 0 + -13

Reorder the terms:
13 + -13 + -7x + x2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -7x + x2 = 0 + -13
-7x + x2 = 0 + -13

Combine like terms: 0 + -13 = -13
-7x + x2 = -13

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = -13 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -13 + 12.25

Combine like terms: -13 + 12.25 = -0.75
12.25 + -7x + x2 = -0.75

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = -0.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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