w^2-19w-210=0

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Solution for w^2-19w-210=0 equation:


Simplifying
w2 + -19w + -210 = 0

Reorder the terms:
-210 + -19w + w2 = 0

Solving
-210 + -19w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '210' to each side of the equation.
-210 + -19w + 210 + w2 = 0 + 210

Reorder the terms:
-210 + 210 + -19w + w2 = 0 + 210

Combine like terms: -210 + 210 = 0
0 + -19w + w2 = 0 + 210
-19w + w2 = 0 + 210

Combine like terms: 0 + 210 = 210
-19w + w2 = 210

The w term is -19w.  Take half its coefficient (-9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
-19w + 90.25 + w2 = 210 + 90.25

Reorder the terms:
90.25 + -19w + w2 = 210 + 90.25

Combine like terms: 210 + 90.25 = 300.25
90.25 + -19w + w2 = 300.25

Factor a perfect square on the left side:
(w + -9.5)(w + -9.5) = 300.25

Calculate the square root of the right side: 17.327723451

Break this problem into two subproblems by setting 
(w + -9.5) equal to 17.327723451 and -17.327723451.


Subproblem 1
w + -9.5 = 17.327723451

Simplifying
w + -9.5 = 17.327723451

Reorder the terms:
-9.5 + w = 17.327723451

Solving
-9.5 + w = 17.327723451

Solving for variable 'w'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + w = 17.327723451 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + w = 17.327723451 + 9.5
w = 17.327723451 + 9.5

Combine like terms: 17.327723451 + 9.5 = 26.827723451
w = 26.827723451

Simplifying
w = 26.827723451


Subproblem 2
w + -9.5 = -17.327723451

Simplifying
w + -9.5 = -17.327723451

Reorder the terms:
-9.5 + w = -17.327723451

Solving
-9.5 + w = -17.327723451

Solving for variable 'w'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + w = -17.327723451 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + w = -17.327723451 + 9.5
w = -17.327723451 + 9.5

Combine like terms: -17.327723451 + 9.5 = -7.827723451
w = -7.827723451

Simplifying
w = -7.827723451


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {26.827723451, -7.827723451}

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