3w^2+7w=38

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Solution for 3w^2+7w=38 equation: 


Simplifying
3w2 + 7w = 38

Reorder the terms:
7w + 3w2 = 38

Solving
7w + 3w2 = 38

Solving for variable 'w'.

Reorder the terms:
-38 + 7w + 3w2 = 38 + -38

Combine like terms: 38 + -38 = 0
-38 + 7w + 3w2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-12.66666667 + 2.333333333w + w2 = 0

Move the constant term to the right:

Add '12.66666667' to each side of the equation.
-12.66666667 + 2.333333333w + 12.66666667 + w2 = 0 + 12.66666667

Reorder the terms:
-12.66666667 + 12.66666667 + 2.333333333w + w2 = 0 + 12.66666667

Combine like terms: -12.66666667 + 12.66666667 = 0.00000000
0.00000000 + 2.333333333w + w2 = 0 + 12.66666667
2.333333333w + w2 = 0 + 12.66666667

Combine like terms: 0 + 12.66666667 = 12.66666667
2.333333333w + w2 = 12.66666667

The w term is 2.333333333w.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333w + 1.361111112 + w2 = 12.66666667 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333w + w2 = 12.66666667 + 1.361111112

Combine like terms: 12.66666667 + 1.361111112 = 14.027777782
1.361111112 + 2.333333333w + w2 = 14.027777782

Factor a perfect square on the left side:
(w + 1.166666667)(w + 1.166666667) = 14.027777782

Calculate the square root of the right side: 3.74536751

Break this problem into two subproblems by setting 
(w + 1.166666667) equal to 3.74536751 and -3.74536751.


Subproblem 1
w + 1.166666667 = 3.74536751

Simplifying
w + 1.166666667 = 3.74536751

Reorder the terms:
1.166666667 + w = 3.74536751

Solving
1.166666667 + w = 3.74536751

Solving for variable 'w'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + w = 3.74536751 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + w = 3.74536751 + -1.166666667
w = 3.74536751 + -1.166666667

Combine like terms: 3.74536751 + -1.166666667 = 2.578700843
w = 2.578700843

Simplifying
w = 2.578700843


Subproblem 2
w + 1.166666667 = -3.74536751

Simplifying
w + 1.166666667 = -3.74536751

Reorder the terms:
1.166666667 + w = -3.74536751

Solving
1.166666667 + w = -3.74536751

Solving for variable 'w'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + w = -3.74536751 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + w = -3.74536751 + -1.166666667
w = -3.74536751 + -1.166666667

Combine like terms: -3.74536751 + -1.166666667 = -4.912034177
w = -4.912034177

Simplifying
w = -4.912034177


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {2.578700843, -4.912034177}

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