w^2-14w-4=0

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Solution for w^2-14w-4=0 equation:


Simplifying
w2 + -14w + -4 = 0

Reorder the terms:
-4 + -14w + w2 = 0

Solving
-4 + -14w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -14w + 4 + w2 = 0 + 4

Reorder the terms:
-4 + 4 + -14w + w2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -14w + w2 = 0 + 4
-14w + w2 = 0 + 4

Combine like terms: 0 + 4 = 4
-14w + w2 = 4

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 = 4 + 49

Reorder the terms:
49 + -14w + w2 = 4 + 49

Combine like terms: 4 + 49 = 53
49 + -14w + w2 = 53

Factor a perfect square on the left side:
(w + -7)(w + -7) = 53

Calculate the square root of the right side: 7.280109889

Break this problem into two subproblems by setting 
(w + -7) equal to 7.280109889 and -7.280109889.

Subproblem 1

w + -7 = 7.280109889 Simplifying w + -7 = 7.280109889 Reorder the terms: -7 + w = 7.280109889 Solving -7 + w = 7.280109889 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 = 7.280109889 + 7 Combine like terms: -7 + 7 = 0 0 + w = 7.280109889 + 7 w = 7.280109889 + 7 Combine like terms: 7.280109889 + 7 = 14.280109889 w = 14.280109889 Simplifying w = 14.280109889

Subproblem 2

w + -7 = -7.280109889 Simplifying w + -7 = -7.280109889 Reorder the terms: -7 + w = -7.280109889 Solving -7 + w = -7.280109889 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 = -7.280109889 + 7 Combine like terms: -7 + 7 = 0 0 + w = -7.280109889 + 7 w = -7.280109889 + 7 Combine like terms: -7.280109889 + 7 = -0.280109889 w = -0.280109889 Simplifying w = -0.280109889

Solution

The solution to the problem is based on the solutions from the subproblems. w = {14.280109889, -0.280109889}

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