2w^2+16w+10=0

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Solution for 2w^2+16w+10=0 equation: 


Simplifying
2w2 + 16w + 10 = 0

Reorder the terms:
10 + 16w + 2w2 = 0

Solving
10 + 16w + 2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 8w + w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + 8w + w2)' equal to zero and attempt to solve:

Simplifying
5 + 8w + w2 = 0

Solving
5 + 8w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 8w + -5 + w2 = 0 + -5

Reorder the terms:
5 + -5 + 8w + w2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 8w + w2 = 0 + -5
8w + w2 = 0 + -5

Combine like terms: 0 + -5 = -5
8w + w2 = -5

The w term is 8w.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8w + 16 + w2 = -5 + 16

Reorder the terms:
16 + 8w + w2 = -5 + 16

Combine like terms: -5 + 16 = 11
16 + 8w + w2 = 11

Factor a perfect square on the left side:
(w + 4)(w + 4) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(w + 4) equal to 3.31662479 and -3.31662479.


Subproblem 1
w + 4 = 3.31662479

Simplifying
w + 4 = 3.31662479

Reorder the terms:
4 + w = 3.31662479

Solving
4 + w = 3.31662479

Solving for variable 'w'.

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

Add '-4' to each side of the equation.
4 + -4 + w = 3.31662479 + -4

Combine like terms: 4 + -4 = 0
0 + w = 3.31662479 + -4
w = 3.31662479 + -4

Combine like terms: 3.31662479 + -4 = -0.68337521
w = -0.68337521

Simplifying
w = -0.68337521


Subproblem 2
w + 4 = -3.31662479

Simplifying
w + 4 = -3.31662479

Reorder the terms:
4 + w = -3.31662479

Solving
4 + w = -3.31662479

Solving for variable 'w'.

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

Add '-4' to each side of the equation.
4 + -4 + w = -3.31662479 + -4

Combine like terms: 4 + -4 = 0
0 + w = -3.31662479 + -4
w = -3.31662479 + -4

Combine like terms: -3.31662479 + -4 = -7.31662479
w = -7.31662479

Simplifying
w = -7.31662479


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-0.68337521, -7.31662479}
Solution
w = {-0.68337521, -7.31662479}

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