0=x^2-12x+45

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Solution for 0=x^2-12x+45 equation:


Simplifying
0 = x2 + -12x + 45

Reorder the terms:
0 = 45 + -12x + x2

Solving
0 = 45 + -12x + x2

Solving for variable 'x'.

Combine like terms: 0 + -45 = -45
-45 + 12x + -1x2 = 45 + -12x + x2 + -45 + 12x + -1x2

Reorder the terms:
-45 + 12x + -1x2 = 45 + -45 + -12x + 12x + x2 + -1x2

Combine like terms: 45 + -45 = 0
-45 + 12x + -1x2 = 0 + -12x + 12x + x2 + -1x2
-45 + 12x + -1x2 = -12x + 12x + x2 + -1x2

Combine like terms: -12x + 12x = 0
-45 + 12x + -1x2 = 0 + x2 + -1x2
-45 + 12x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-45 + 12x + -1x2 = 0

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

Divide each side by '-1'.
45 + -12x + x2 = 0

Move the constant term to the right:

Add '-45' to each side of the equation.
45 + -12x + -45 + x2 = 0 + -45

Reorder the terms:
45 + -45 + -12x + x2 = 0 + -45

Combine like terms: 45 + -45 = 0
0 + -12x + x2 = 0 + -45
-12x + x2 = 0 + -45

Combine like terms: 0 + -45 = -45
-12x + x2 = -45

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -45 + 36

Reorder the terms:
36 + -12x + x2 = -45 + 36

Combine like terms: -45 + 36 = -9
36 + -12x + x2 = -9

Factor a perfect square on the left side:
(x + -6)(x + -6) = -9

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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