x^2+-6x+-21=0

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

Simplifying
x2 + -6x + -21 = 0

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

Solving
-21 + -6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

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 = 30
9 + -6x + x2 = 30

Factor a perfect square on the left side:
(x + -3)(x + -3) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(x + -3) equal to 5.477225575 and -5.477225575.

Subproblem 1
x + -3 = 5.477225575

Simplifying
x + -3 = 5.477225575

Reorder the terms:
-3 + x = 5.477225575

Solving
-3 + x = 5.477225575

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + x = 5.477225575 + 3

Combine like terms: -3 + 3 = 0
0 + x = 5.477225575 + 3
x = 5.477225575 + 3

Combine like terms: 5.477225575 + 3 = 8.477225575
x = 8.477225575

Simplifying
x = 8.477225575

Subproblem 2
x + -3 = -5.477225575

Simplifying
x + -3 = -5.477225575

Reorder the terms:
-3 + x = -5.477225575

Solving
-3 + x = -5.477225575

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + x = -5.477225575 + 3

Combine like terms: -3 + 3 = 0
0 + x = -5.477225575 + 3
x = -5.477225575 + 3

Combine like terms: -5.477225575 + 3 = -2.477225575
x = -2.477225575

Simplifying
x = -2.477225575

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.477225575, -2.477225575}