w^2-13w=42

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Solution for w^2-13w=42 equation:


Simplifying
w2 + -13w = 42

Reorder the terms:
-13w + w2 = 42

Solving
-13w + w2 = 42

Solving for variable 'w'.

Reorder the terms:
-42 + -13w + w2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + -13w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '42' to each side of the equation.
-42 + -13w + 42 + w2 = 0 + 42

Reorder the terms:
-42 + 42 + -13w + w2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + -13w + w2 = 0 + 42
-13w + w2 = 0 + 42

Combine like terms: 0 + 42 = 42
-13w + w2 = 42

The w term is -13w.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13w + 42.25 + w2 = 42 + 42.25

Reorder the terms:
42.25 + -13w + w2 = 42 + 42.25

Combine like terms: 42 + 42.25 = 84.25
42.25 + -13w + w2 = 84.25

Factor a perfect square on the left side:
(w + -6.5)(w + -6.5) = 84.25

Calculate the square root of the right side: 9.178779875

Break this problem into two subproblems by setting 
(w + -6.5) equal to 9.178779875 and -9.178779875.

Subproblem 1

w + -6.5 = 9.178779875 Simplifying w + -6.5 = 9.178779875 Reorder the terms: -6.5 + w = 9.178779875 Solving -6.5 + w = 9.178779875 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + w = 9.178779875 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + w = 9.178779875 + 6.5 w = 9.178779875 + 6.5 Combine like terms: 9.178779875 + 6.5 = 15.678779875 w = 15.678779875 Simplifying w = 15.678779875

Subproblem 2

w + -6.5 = -9.178779875 Simplifying w + -6.5 = -9.178779875 Reorder the terms: -6.5 + w = -9.178779875 Solving -6.5 + w = -9.178779875 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + w = -9.178779875 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + w = -9.178779875 + 6.5 w = -9.178779875 + 6.5 Combine like terms: -9.178779875 + 6.5 = -2.678779875 w = -2.678779875 Simplifying w = -2.678779875

Solution

The solution to the problem is based on the solutions from the subproblems. w = {15.678779875, -2.678779875}

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