0=x^2-6x+21

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Solution for 0=x^2-6x+21 equation:


Simplifying
0 = x2 + -6x + 21

Reorder the terms:
0 = 21 + -6x + x2

Solving
0 = 21 + -6x + x2

Solving for variable 'x'.

Combine like terms: 0 + -21 = -21
-21 + 6x + -1x2 = 21 + -6x + x2 + -21 + 6x + -1x2

Reorder the terms:
-21 + 6x + -1x2 = 21 + -21 + -6x + 6x + x2 + -1x2

Combine like terms: 21 + -21 = 0
-21 + 6x + -1x2 = 0 + -6x + 6x + x2 + -1x2
-21 + 6x + -1x2 = -6x + 6x + x2 + -1x2

Combine like terms: -6x + 6x = 0
-21 + 6x + -1x2 = 0 + x2 + -1x2
-21 + 6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-21 + 6x + -1x2 = 0

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

Divide each side by '-1'.
21 + -6x + x2 = 0

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + -6x + -21 + x2 = 0 + -21

Reorder the terms:
21 + -21 + -6x + x2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -6x + x2 = 0 + -21
-6x + x2 = 0 + -21

Combine like terms: 0 + -21 = -21
-6x + x2 = -21

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -21 + 9

Reorder the terms:
9 + -6x + x2 = -21 + 9

Combine like terms: -21 + 9 = -12
9 + -6x + x2 = -12

Factor a perfect square on the left side:
(x + -3)(x + -3) = -12

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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