w^2-14w-5=0

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Solution for w^2-14w-5=0 equation:


Simplifying
w2 + -14w + -5 = 0

Reorder the terms:
-5 + -14w + w2 = 0

Solving
-5 + -14w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -14w + 5 + w2 = 0 + 5

Reorder the terms:
-5 + 5 + -14w + w2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -14w + w2 = 0 + 5
-14w + w2 = 0 + 5

Combine like terms: 0 + 5 = 5
-14w + w2 = 5

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 = 5 + 49

Reorder the terms:
49 + -14w + w2 = 5 + 49

Combine like terms: 5 + 49 = 54
49 + -14w + w2 = 54

Factor a perfect square on the left side:
(w + -7)(w + -7) = 54

Calculate the square root of the right side: 7.348469228

Break this problem into two subproblems by setting 
(w + -7) equal to 7.348469228 and -7.348469228.

Subproblem 1

w + -7 = 7.348469228 Simplifying w + -7 = 7.348469228 Reorder the terms: -7 + w = 7.348469228 Solving -7 + w = 7.348469228 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 = 7.348469228 + 7 Combine like terms: -7 + 7 = 0 0 + w = 7.348469228 + 7 w = 7.348469228 + 7 Combine like terms: 7.348469228 + 7 = 14.348469228 w = 14.348469228 Simplifying w = 14.348469228

Subproblem 2

w + -7 = -7.348469228 Simplifying w + -7 = -7.348469228 Reorder the terms: -7 + w = -7.348469228 Solving -7 + w = -7.348469228 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 = -7.348469228 + 7 Combine like terms: -7 + 7 = 0 0 + w = -7.348469228 + 7 w = -7.348469228 + 7 Combine like terms: -7.348469228 + 7 = -0.348469228 w = -0.348469228 Simplifying w = -0.348469228

Solution

The solution to the problem is based on the solutions from the subproblems. w = {14.348469228, -0.348469228}

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