4(w^2+10w+13)=0

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Solution for 4(w^2+10w+13)=0 equation: 


Simplifying
4(w2 + 10w + 13) = 0

Reorder the terms:
4(13 + 10w + w2) = 0
(13 * 4 + 10w * 4 + w2 * 4) = 0
(52 + 40w + 4w2) = 0

Solving
52 + 40w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '4'.
4(13 + 10w + w2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(13 + 10w + w2)' equal to zero and attempt to solve:

Simplifying
13 + 10w + w2 = 0

Solving
13 + 10w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + 10w + -13 + w2 = 0 + -13

Reorder the terms:
13 + -13 + 10w + w2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 10w + w2 = 0 + -13
10w + w2 = 0 + -13

Combine like terms: 0 + -13 = -13
10w + w2 = -13

The w term is 10w.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10w + 25 + w2 = -13 + 25

Reorder the terms:
25 + 10w + w2 = -13 + 25

Combine like terms: -13 + 25 = 12
25 + 10w + w2 = 12

Factor a perfect square on the left side:
(w + 5)(w + 5) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(w + 5) equal to 3.464101615 and -3.464101615.


Subproblem 1
w + 5 = 3.464101615

Simplifying
w + 5 = 3.464101615

Reorder the terms:
5 + w = 3.464101615

Solving
5 + w = 3.464101615

Solving for variable 'w'.

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

Add '-5' to each side of the equation.
5 + -5 + w = 3.464101615 + -5

Combine like terms: 5 + -5 = 0
0 + w = 3.464101615 + -5
w = 3.464101615 + -5

Combine like terms: 3.464101615 + -5 = -1.535898385
w = -1.535898385

Simplifying
w = -1.535898385


Subproblem 2
w + 5 = -3.464101615

Simplifying
w + 5 = -3.464101615

Reorder the terms:
5 + w = -3.464101615

Solving
5 + w = -3.464101615

Solving for variable 'w'.

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

Add '-5' to each side of the equation.
5 + -5 + w = -3.464101615 + -5

Combine like terms: 5 + -5 = 0
0 + w = -3.464101615 + -5
w = -3.464101615 + -5

Combine like terms: -3.464101615 + -5 = -8.464101615
w = -8.464101615

Simplifying
w = -8.464101615


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-1.535898385, -8.464101615}
Solution
w = {-1.535898385, -8.464101615}

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