w(w+2)=52

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Solution for w(w+2)=52 equation:


Simplifying
w(w + 2) = 52

Reorder the terms:
w(2 + w) = 52
(2 * w + w * w) = 52
(2w + w2) = 52

Solving
2w + w2 = 52

Solving for variable 'w'.

Reorder the terms:
-52 + 2w + w2 = 52 + -52

Combine like terms: 52 + -52 = 0
-52 + 2w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '52' to each side of the equation.
-52 + 2w + 52 + w2 = 0 + 52

Reorder the terms:
-52 + 52 + 2w + w2 = 0 + 52

Combine like terms: -52 + 52 = 0
0 + 2w + w2 = 0 + 52
2w + w2 = 0 + 52

Combine like terms: 0 + 52 = 52
2w + w2 = 52

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 = 52 + 1

Reorder the terms:
1 + 2w + w2 = 52 + 1

Combine like terms: 52 + 1 = 53
1 + 2w + w2 = 53

Factor a perfect square on the left side:
(w + 1)(w + 1) = 53

Calculate the square root of the right side: 7.280109889

Break this problem into two subproblems by setting 
(w + 1) equal to 7.280109889 and -7.280109889.

Subproblem 1

w + 1 = 7.280109889 Simplifying w + 1 = 7.280109889 Reorder the terms: 1 + w = 7.280109889 Solving 1 + w = 7.280109889 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 = 7.280109889 + -1 Combine like terms: 1 + -1 = 0 0 + w = 7.280109889 + -1 w = 7.280109889 + -1 Combine like terms: 7.280109889 + -1 = 6.280109889 w = 6.280109889 Simplifying w = 6.280109889

Subproblem 2

w + 1 = -7.280109889 Simplifying w + 1 = -7.280109889 Reorder the terms: 1 + w = -7.280109889 Solving 1 + w = -7.280109889 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 = -7.280109889 + -1 Combine like terms: 1 + -1 = 0 0 + w = -7.280109889 + -1 w = -7.280109889 + -1 Combine like terms: -7.280109889 + -1 = -8.280109889 w = -8.280109889 Simplifying w = -8.280109889

Solution

The solution to the problem is based on the solutions from the subproblems. w = {6.280109889, -8.280109889}

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