2w(w+3)=560

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Solution for 2w(w+3)=560 equation: 


Simplifying
2w(w + 3) = 560

Reorder the terms:
2w(3 + w) = 560
(3 * 2w + w * 2w) = 560
(6w + 2w2) = 560

Solving
6w + 2w2 = 560

Solving for variable 'w'.

Reorder the terms:
-560 + 6w + 2w2 = 560 + -560

Combine like terms: 560 + -560 = 0
-560 + 6w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-280 + 3w + w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-280 + 3w + w2)' equal to zero and attempt to solve:

Simplifying
-280 + 3w + w2 = 0

Solving
-280 + 3w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '280' to each side of the equation.
-280 + 3w + 280 + w2 = 0 + 280

Reorder the terms:
-280 + 280 + 3w + w2 = 0 + 280

Combine like terms: -280 + 280 = 0
0 + 3w + w2 = 0 + 280
3w + w2 = 0 + 280

Combine like terms: 0 + 280 = 280
3w + w2 = 280

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 = 280 + 2.25

Reorder the terms:
2.25 + 3w + w2 = 280 + 2.25

Combine like terms: 280 + 2.25 = 282.25
2.25 + 3w + w2 = 282.25

Factor a perfect square on the left side:
(w + 1.5)(w + 1.5) = 282.25

Calculate the square root of the right side: 16.800297616

Break this problem into two subproblems by setting 
(w + 1.5) equal to 16.800297616 and -16.800297616.


Subproblem 1
w + 1.5 = 16.800297616

Simplifying
w + 1.5 = 16.800297616

Reorder the terms:
1.5 + w = 16.800297616

Solving
1.5 + w = 16.800297616

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 = 16.800297616 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = 16.800297616 + -1.5
w = 16.800297616 + -1.5

Combine like terms: 16.800297616 + -1.5 = 15.300297616
w = 15.300297616

Simplifying
w = 15.300297616


Subproblem 2
w + 1.5 = -16.800297616

Simplifying
w + 1.5 = -16.800297616

Reorder the terms:
1.5 + w = -16.800297616

Solving
1.5 + w = -16.800297616

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 = -16.800297616 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = -16.800297616 + -1.5
w = -16.800297616 + -1.5

Combine like terms: -16.800297616 + -1.5 = -18.300297616
w = -18.300297616

Simplifying
w = -18.300297616


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {15.300297616, -18.300297616}
Solution
w = {15.300297616, -18.300297616}

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