w(w+3)=58

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Solution for w(w+3)=58 equation:


Simplifying
w(w + 3) = 58

Reorder the terms:
w(3 + w) = 58
(3 * w + w * w) = 58
(3w + w2) = 58

Solving
3w + w2 = 58

Solving for variable 'w'.

Reorder the terms:
-58 + 3w + w2 = 58 + -58

Combine like terms: 58 + -58 = 0
-58 + 3w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '58' to each side of the equation.
-58 + 3w + 58 + w2 = 0 + 58

Reorder the terms:
-58 + 58 + 3w + w2 = 0 + 58

Combine like terms: -58 + 58 = 0
0 + 3w + w2 = 0 + 58
3w + w2 = 0 + 58

Combine like terms: 0 + 58 = 58
3w + w2 = 58

The w term is 3w.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3w + 2.25 + w2 = 58 + 2.25

Reorder the terms:
2.25 + 3w + w2 = 58 + 2.25

Combine like terms: 58 + 2.25 = 60.25
2.25 + 3w + w2 = 60.25

Factor a perfect square on the left side:
(w + 1.5)(w + 1.5) = 60.25

Calculate the square root of the right side: 7.762087348

Break this problem into two subproblems by setting 
(w + 1.5) equal to 7.762087348 and -7.762087348.


Subproblem 1
w + 1.5 = 7.762087348

Simplifying
w + 1.5 = 7.762087348

Reorder the terms:
1.5 + w = 7.762087348

Solving
1.5 + w = 7.762087348

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '-1.5' to each side of the equation.
1.5 + -1.5 + w = 7.762087348 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = 7.762087348 + -1.5
w = 7.762087348 + -1.5

Combine like terms: 7.762087348 + -1.5 = 6.262087348
w = 6.262087348

Simplifying
w = 6.262087348


Subproblem 2
w + 1.5 = -7.762087348

Simplifying
w + 1.5 = -7.762087348

Reorder the terms:
1.5 + w = -7.762087348

Solving
1.5 + w = -7.762087348

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '-1.5' to each side of the equation.
1.5 + -1.5 + w = -7.762087348 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = -7.762087348 + -1.5
w = -7.762087348 + -1.5

Combine like terms: -7.762087348 + -1.5 = -9.262087348
w = -9.262087348

Simplifying
w = -9.262087348


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {6.262087348, -9.262087348}

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