(w+5)(w)=33

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Solution for (w+5)(w)=33 equation: 


Simplifying
(w + 5)(w) = 33

Reorder the terms:
(5 + w)(w) = 33

Reorder the terms for easier multiplication:
w(5 + w) = 33
(5 * w + w * w) = 33
(5w + w2) = 33

Solving
5w + w2 = 33

Solving for variable 'w'.

Reorder the terms:
-33 + 5w + w2 = 33 + -33

Combine like terms: 33 + -33 = 0
-33 + 5w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + 5w + 33 + w2 = 0 + 33

Reorder the terms:
-33 + 33 + 5w + w2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + 5w + w2 = 0 + 33
5w + w2 = 0 + 33

Combine like terms: 0 + 33 = 33
5w + w2 = 33

The w term is 5w.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5w + 6.25 + w2 = 33 + 6.25

Reorder the terms:
6.25 + 5w + w2 = 33 + 6.25

Combine like terms: 33 + 6.25 = 39.25
6.25 + 5w + w2 = 39.25

Factor a perfect square on the left side:
(w + 2.5)(w + 2.5) = 39.25

Calculate the square root of the right side: 6.264982043

Break this problem into two subproblems by setting 
(w + 2.5) equal to 6.264982043 and -6.264982043.


Subproblem 1
w + 2.5 = 6.264982043

Simplifying
w + 2.5 = 6.264982043

Reorder the terms:
2.5 + w = 6.264982043

Solving
2.5 + w = 6.264982043

Solving for variable 'w'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + w = 6.264982043 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = 6.264982043 + -2.5
w = 6.264982043 + -2.5

Combine like terms: 6.264982043 + -2.5 = 3.764982043
w = 3.764982043

Simplifying
w = 3.764982043


Subproblem 2
w + 2.5 = -6.264982043

Simplifying
w + 2.5 = -6.264982043

Reorder the terms:
2.5 + w = -6.264982043

Solving
2.5 + w = -6.264982043

Solving for variable 'w'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + w = -6.264982043 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = -6.264982043 + -2.5
w = -6.264982043 + -2.5

Combine like terms: -6.264982043 + -2.5 = -8.764982043
w = -8.764982043

Simplifying
w = -8.764982043


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {3.764982043, -8.764982043}

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