(2w+18)(w-4)=84

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Solution for (2w+18)(w-4)=84 equation: 


Simplifying
(2w + 18)(w + -4) = 84

Reorder the terms:
(18 + 2w)(w + -4) = 84

Reorder the terms:
(18 + 2w)(-4 + w) = 84

Multiply (18 + 2w) * (-4 + w)
(18(-4 + w) + 2w * (-4 + w)) = 84
((-4 * 18 + w * 18) + 2w * (-4 + w)) = 84
((-72 + 18w) + 2w * (-4 + w)) = 84
(-72 + 18w + (-4 * 2w + w * 2w)) = 84
(-72 + 18w + (-8w + 2w2)) = 84

Combine like terms: 18w + -8w = 10w
(-72 + 10w + 2w2) = 84

Solving
-72 + 10w + 2w2 = 84

Solving for variable 'w'.

Reorder the terms:
-72 + -84 + 10w + 2w2 = 84 + -84

Combine like terms: -72 + -84 = -156
-156 + 10w + 2w2 = 84 + -84

Combine like terms: 84 + -84 = 0
-156 + 10w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-78 + 5w + w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-78 + 5w + w2)' equal to zero and attempt to solve:

Simplifying
-78 + 5w + w2 = 0

Solving
-78 + 5w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '78' to each side of the equation.
-78 + 5w + 78 + w2 = 0 + 78

Reorder the terms:
-78 + 78 + 5w + w2 = 0 + 78

Combine like terms: -78 + 78 = 0
0 + 5w + w2 = 0 + 78
5w + w2 = 0 + 78

Combine like terms: 0 + 78 = 78
5w + w2 = 78

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 = 78 + 6.25

Reorder the terms:
6.25 + 5w + w2 = 78 + 6.25

Combine like terms: 78 + 6.25 = 84.25
6.25 + 5w + w2 = 84.25

Factor a perfect square on the left side:
(w + 2.5)(w + 2.5) = 84.25

Calculate the square root of the right side: 9.178779875

Break this problem into two subproblems by setting 
(w + 2.5) equal to 9.178779875 and -9.178779875.


Subproblem 1
w + 2.5 = 9.178779875

Simplifying
w + 2.5 = 9.178779875

Reorder the terms:
2.5 + w = 9.178779875

Solving
2.5 + w = 9.178779875

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 = 9.178779875 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = 9.178779875 + -2.5
w = 9.178779875 + -2.5

Combine like terms: 9.178779875 + -2.5 = 6.678779875
w = 6.678779875

Simplifying
w = 6.678779875


Subproblem 2
w + 2.5 = -9.178779875

Simplifying
w + 2.5 = -9.178779875

Reorder the terms:
2.5 + w = -9.178779875

Solving
2.5 + w = -9.178779875

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 = -9.178779875 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = -9.178779875 + -2.5
w = -9.178779875 + -2.5

Combine like terms: -9.178779875 + -2.5 = -11.678779875
w = -11.678779875

Simplifying
w = -11.678779875


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {6.678779875, -11.678779875}
Solution
w = {6.678779875, -11.678779875}

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