2w*(w+7)=50

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Solution for 2w*(w+7)=50 equation: 


Simplifying
2w(w + 7) = 50

Reorder the terms:
2w(7 + w) = 50
(7 * 2w + w * 2w) = 50
(14w + 2w2) = 50

Solving
14w + 2w2 = 50

Solving for variable 'w'.

Reorder the terms:
-50 + 14w + 2w2 = 50 + -50

Combine like terms: 50 + -50 = 0
-50 + 14w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-25 + 7w + w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-25 + 7w + w2)' equal to zero and attempt to solve:

Simplifying
-25 + 7w + w2 = 0

Solving
-25 + 7w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 7w + 25 + w2 = 0 + 25

Reorder the terms:
-25 + 25 + 7w + w2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 7w + w2 = 0 + 25
7w + w2 = 0 + 25

Combine like terms: 0 + 25 = 25
7w + w2 = 25

The w term is 7w.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7w + 12.25 + w2 = 25 + 12.25

Reorder the terms:
12.25 + 7w + w2 = 25 + 12.25

Combine like terms: 25 + 12.25 = 37.25
12.25 + 7w + w2 = 37.25

Factor a perfect square on the left side:
(w + 3.5)(w + 3.5) = 37.25

Calculate the square root of the right side: 6.103277808

Break this problem into two subproblems by setting 
(w + 3.5) equal to 6.103277808 and -6.103277808.


Subproblem 1
w + 3.5 = 6.103277808

Simplifying
w + 3.5 = 6.103277808

Reorder the terms:
3.5 + w = 6.103277808

Solving
3.5 + w = 6.103277808

Solving for variable 'w'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + w = 6.103277808 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + w = 6.103277808 + -3.5
w = 6.103277808 + -3.5

Combine like terms: 6.103277808 + -3.5 = 2.603277808
w = 2.603277808

Simplifying
w = 2.603277808


Subproblem 2
w + 3.5 = -6.103277808

Simplifying
w + 3.5 = -6.103277808

Reorder the terms:
3.5 + w = -6.103277808

Solving
3.5 + w = -6.103277808

Solving for variable 'w'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + w = -6.103277808 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + w = -6.103277808 + -3.5
w = -6.103277808 + -3.5

Combine like terms: -6.103277808 + -3.5 = -9.603277808
w = -9.603277808

Simplifying
w = -9.603277808


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {2.603277808, -9.603277808}
Solution
w = {2.603277808, -9.603277808}

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