w(w-2)=40

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Solution for w(w-2)=40 equation:


Simplifying
w(w + -2) = 40

Reorder the terms:
w(-2 + w) = 40
(-2 * w + w * w) = 40
(-2w + w2) = 40

Solving
-2w + w2 = 40

Solving for variable 'w'.

Reorder the terms:
-40 + -2w + w2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + -2w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -2w + 40 + w2 = 0 + 40

Reorder the terms:
-40 + 40 + -2w + w2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -2w + w2 = 0 + 40
-2w + w2 = 0 + 40

Combine like terms: 0 + 40 = 40
-2w + w2 = 40

The w term is -2w.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2w + 1 + w2 = 40 + 1

Reorder the terms:
1 + -2w + w2 = 40 + 1

Combine like terms: 40 + 1 = 41
1 + -2w + w2 = 41

Factor a perfect square on the left side:
(w + -1)(w + -1) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(w + -1) equal to 6.403124237 and -6.403124237.

Subproblem 1

w + -1 = 6.403124237 Simplifying w + -1 = 6.403124237 Reorder the terms: -1 + w = 6.403124237 Solving -1 + w = 6.403124237 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = 6.403124237 + 1 Combine like terms: -1 + 1 = 0 0 + w = 6.403124237 + 1 w = 6.403124237 + 1 Combine like terms: 6.403124237 + 1 = 7.403124237 w = 7.403124237 Simplifying w = 7.403124237

Subproblem 2

w + -1 = -6.403124237 Simplifying w + -1 = -6.403124237 Reorder the terms: -1 + w = -6.403124237 Solving -1 + w = -6.403124237 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = -6.403124237 + 1 Combine like terms: -1 + 1 = 0 0 + w = -6.403124237 + 1 w = -6.403124237 + 1 Combine like terms: -6.403124237 + 1 = -5.403124237 w = -5.403124237 Simplifying w = -5.403124237

Solution

The solution to the problem is based on the solutions from the subproblems. w = {7.403124237, -5.403124237}

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