w^2-14w-14=0

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Solution for w^2-14w-14=0 equation: 


Simplifying
w2 + -14w + -14 = 0

Reorder the terms:
-14 + -14w + w2 = 0

Solving
-14 + -14w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -14w + 14 + w2 = 0 + 14

Reorder the terms:
-14 + 14 + -14w + w2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -14w + w2 = 0 + 14
-14w + w2 = 0 + 14

Combine like terms: 0 + 14 = 14
-14w + w2 = 14

The w term is -14w.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14w + 49 + w2 = 14 + 49

Reorder the terms:
49 + -14w + w2 = 14 + 49

Combine like terms: 14 + 49 = 63
49 + -14w + w2 = 63

Factor a perfect square on the left side:
(w + -7)(w + -7) = 63

Calculate the square root of the right side: 7.937253933

Break this problem into two subproblems by setting 
(w + -7) equal to 7.937253933 and -7.937253933.


Subproblem 1
w + -7 = 7.937253933

Simplifying
w + -7 = 7.937253933

Reorder the terms:
-7 + w = 7.937253933

Solving
-7 + w = 7.937253933

Solving for variable 'w'.

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

Add '7' to each side of the equation.
-7 + 7 + w = 7.937253933 + 7

Combine like terms: -7 + 7 = 0
0 + w = 7.937253933 + 7
w = 7.937253933 + 7

Combine like terms: 7.937253933 + 7 = 14.937253933
w = 14.937253933

Simplifying
w = 14.937253933


Subproblem 2
w + -7 = -7.937253933

Simplifying
w + -7 = -7.937253933

Reorder the terms:
-7 + w = -7.937253933

Solving
-7 + w = -7.937253933

Solving for variable 'w'.

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

Add '7' to each side of the equation.
-7 + 7 + w = -7.937253933 + 7

Combine like terms: -7 + 7 = 0
0 + w = -7.937253933 + 7
w = -7.937253933 + 7

Combine like terms: -7.937253933 + 7 = -0.937253933
w = -0.937253933

Simplifying
w = -0.937253933


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {14.937253933, -0.937253933}

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