w^2-28w=-31

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Solution for w^2-28w=-31 equation:


Simplifying
w2 + -28w = -31

Reorder the terms:
-28w + w2 = -31

Solving
-28w + w2 = -31

Solving for variable 'w'.

Reorder the terms:
31 + -28w + w2 = -31 + 31

Combine like terms: -31 + 31 = 0
31 + -28w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-31' to each side of the equation.
31 + -28w + -31 + w2 = 0 + -31

Reorder the terms:
31 + -31 + -28w + w2 = 0 + -31

Combine like terms: 31 + -31 = 0
0 + -28w + w2 = 0 + -31
-28w + w2 = 0 + -31

Combine like terms: 0 + -31 = -31
-28w + w2 = -31

The w term is -28w.  Take half its coefficient (-14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
-28w + 196 + w2 = -31 + 196

Reorder the terms:
196 + -28w + w2 = -31 + 196

Combine like terms: -31 + 196 = 165
196 + -28w + w2 = 165

Factor a perfect square on the left side:
(w + -14)(w + -14) = 165

Calculate the square root of the right side: 12.845232579

Break this problem into two subproblems by setting 
(w + -14) equal to 12.845232579 and -12.845232579.

Subproblem 1

w + -14 = 12.845232579 Simplifying w + -14 = 12.845232579 Reorder the terms: -14 + w = 12.845232579 Solving -14 + w = 12.845232579 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + w = 12.845232579 + 14 Combine like terms: -14 + 14 = 0 0 + w = 12.845232579 + 14 w = 12.845232579 + 14 Combine like terms: 12.845232579 + 14 = 26.845232579 w = 26.845232579 Simplifying w = 26.845232579

Subproblem 2

w + -14 = -12.845232579 Simplifying w + -14 = -12.845232579 Reorder the terms: -14 + w = -12.845232579 Solving -14 + w = -12.845232579 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + w = -12.845232579 + 14 Combine like terms: -14 + 14 = 0 0 + w = -12.845232579 + 14 w = -12.845232579 + 14 Combine like terms: -12.845232579 + 14 = 1.154767421 w = 1.154767421 Simplifying w = 1.154767421

Solution

The solution to the problem is based on the solutions from the subproblems. w = {26.845232579, 1.154767421}

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