w(10+6w)=7

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Solution for w(10+6w)=7 equation: 


Simplifying
w(10 + 6w) = 7
(10 * w + 6w * w) = 7
(10w + 6w2) = 7

Solving
10w + 6w2 = 7

Solving for variable 'w'.

Reorder the terms:
-7 + 10w + 6w2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 10w + 6w2 = 0

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

Divide each side by '6'.
-1.166666667 + 1.666666667w + w2 = 0

Move the constant term to the right:

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.666666667w + 1.166666667 + w2 = 0 + 1.166666667

Reorder the terms:
-1.166666667 + 1.166666667 + 1.666666667w + w2 = 0 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + 1.666666667w + w2 = 0 + 1.166666667
1.666666667w + w2 = 0 + 1.166666667

Combine like terms: 0 + 1.166666667 = 1.166666667
1.666666667w + w2 = 1.166666667

The w term is 1.666666667w.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667w + 0.6944444447 + w2 = 1.166666667 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667w + w2 = 1.166666667 + 0.6944444447

Combine like terms: 1.166666667 + 0.6944444447 = 1.8611111117
0.6944444447 + 1.666666667w + w2 = 1.8611111117

Factor a perfect square on the left side:
(w + 0.8333333335)(w + 0.8333333335) = 1.8611111117

Calculate the square root of the right side: 1.364225462

Break this problem into two subproblems by setting 
(w + 0.8333333335) equal to 1.364225462 and -1.364225462.


Subproblem 1
w + 0.8333333335 = 1.364225462

Simplifying
w + 0.8333333335 = 1.364225462

Reorder the terms:
0.8333333335 + w = 1.364225462

Solving
0.8333333335 + w = 1.364225462

Solving for variable 'w'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + w = 1.364225462 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + w = 1.364225462 + -0.8333333335
w = 1.364225462 + -0.8333333335

Combine like terms: 1.364225462 + -0.8333333335 = 0.5308921285
w = 0.5308921285

Simplifying
w = 0.5308921285


Subproblem 2
w + 0.8333333335 = -1.364225462

Simplifying
w + 0.8333333335 = -1.364225462

Reorder the terms:
0.8333333335 + w = -1.364225462

Solving
0.8333333335 + w = -1.364225462

Solving for variable 'w'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + w = -1.364225462 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + w = -1.364225462 + -0.8333333335
w = -1.364225462 + -0.8333333335

Combine like terms: -1.364225462 + -0.8333333335 = -2.1975587955
w = -2.1975587955

Simplifying
w = -2.1975587955


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.5308921285, -2.1975587955}

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