w^2-14w+39=0

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Solution for w^2-14w+39=0 equation:


Simplifying
w2 + -14w + 39 = 0

Reorder the terms:
39 + -14w + w2 = 0

Solving
39 + -14w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '-39' to each side of the equation.
39 + -14w + -39 + w2 = 0 + -39

Reorder the terms:
39 + -39 + -14w + w2 = 0 + -39

Combine like terms: 39 + -39 = 0
0 + -14w + w2 = 0 + -39
-14w + w2 = 0 + -39

Combine like terms: 0 + -39 = -39
-14w + w2 = -39

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 = -39 + 49

Reorder the terms:
49 + -14w + w2 = -39 + 49

Combine like terms: -39 + 49 = 10
49 + -14w + w2 = 10

Factor a perfect square on the left side:
(w + -7)(w + -7) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(w + -7) equal to 3.16227766 and -3.16227766.

Subproblem 1

w + -7 = 3.16227766 Simplifying w + -7 = 3.16227766 Reorder the terms: -7 + w = 3.16227766 Solving -7 + w = 3.16227766 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 = 3.16227766 + 7 Combine like terms: -7 + 7 = 0 0 + w = 3.16227766 + 7 w = 3.16227766 + 7 Combine like terms: 3.16227766 + 7 = 10.16227766 w = 10.16227766 Simplifying w = 10.16227766

Subproblem 2

w + -7 = -3.16227766 Simplifying w + -7 = -3.16227766 Reorder the terms: -7 + w = -3.16227766 Solving -7 + w = -3.16227766 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 = -3.16227766 + 7 Combine like terms: -7 + 7 = 0 0 + w = -3.16227766 + 7 w = -3.16227766 + 7 Combine like terms: -3.16227766 + 7 = 3.83772234 w = 3.83772234 Simplifying w = 3.83772234

Solution

The solution to the problem is based on the solutions from the subproblems. w = {10.16227766, 3.83772234}

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