w^2-w-21=10

Solution for w^2-w-21=10 equation:

Simplifying
w2 + -1w + -21 = 10

Reorder the terms:
-21 + -1w + w2 = 10

Solving
-21 + -1w + w2 = 10

Solving for variable 'w'.

Reorder the terms:
-21 + -10 + -1w + w2 = 10 + -10

Combine like terms: -21 + -10 = -31
-31 + -1w + w2 = 10 + -10

Combine like terms: 10 + -10 = 0
-31 + -1w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + -1w + 31 + w2 = 0 + 31

Reorder the terms:
-31 + 31 + -1w + w2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -1w + w2 = 0 + 31
-1w + w2 = 0 + 31

Combine like terms: 0 + 31 = 31
-1w + w2 = 31

The w term is -1w.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1w + 0.25 + w2 = 31 + 0.25

Reorder the terms:
0.25 + -1w + w2 = 31 + 0.25

Combine like terms: 31 + 0.25 = 31.25
0.25 + -1w + w2 = 31.25

Factor a perfect square on the left side:
(w + -0.5)(w + -0.5) = 31.25

Calculate the square root of the right side: 5.590169944

Break this problem into two subproblems by setting 
(w + -0.5) equal to 5.590169944 and -5.590169944.

Subproblem 1
w + -0.5 = 5.590169944

Simplifying
w + -0.5 = 5.590169944

Reorder the terms:
-0.5 + w = 5.590169944

Solving
-0.5 + w = 5.590169944

Solving for variable 'w'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + w = 5.590169944 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + w = 5.590169944 + 0.5
w = 5.590169944 + 0.5

Combine like terms: 5.590169944 + 0.5 = 6.090169944
w = 6.090169944

Simplifying
w = 6.090169944

Subproblem 2
w + -0.5 = -5.590169944

Simplifying
w + -0.5 = -5.590169944

Reorder the terms:
-0.5 + w = -5.590169944

Solving
-0.5 + w = -5.590169944

Solving for variable 'w'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + w = -5.590169944 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + w = -5.590169944 + 0.5
w = -5.590169944 + 0.5

Combine like terms: -5.590169944 + 0.5 = -5.090169944
w = -5.090169944

Simplifying
w = -5.090169944

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {6.090169944, -5.090169944}