-3w^2=14w+5

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Solution for -3w^2=14w+5 equation: 


Simplifying
-3w2 = 14w + 5

Reorder the terms:
-3w2 = 5 + 14w

Solving
-3w2 = 5 + 14w

Solving for variable 'w'.

Reorder the terms:
-5 + -14w + -3w2 = 5 + 14w + -5 + -14w

Reorder the terms:
-5 + -14w + -3w2 = 5 + -5 + 14w + -14w

Combine like terms: 5 + -5 = 0
-5 + -14w + -3w2 = 0 + 14w + -14w
-5 + -14w + -3w2 = 14w + -14w

Combine like terms: 14w + -14w = 0
-5 + -14w + -3w2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 14w + 3w2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + 14w + 3w2)' equal to zero and attempt to solve:

Simplifying
5 + 14w + 3w2 = 0

Solving
5 + 14w + 3w2 = 0

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

Divide each side by '3'.
1.666666667 + 4.666666667w + w2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + 4.666666667w + -1.666666667 + w2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + 4.666666667w + w2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + 4.666666667w + w2 = 0 + -1.666666667
4.666666667w + w2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
4.666666667w + w2 = -1.666666667

The w term is 4.666666667w.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667w + 5.444444448 + w2 = -1.666666667 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667w + w2 = -1.666666667 + 5.444444448

Combine like terms: -1.666666667 + 5.444444448 = 3.777777781
5.444444448 + 4.666666667w + w2 = 3.777777781

Factor a perfect square on the left side:
(w + 2.333333334)(w + 2.333333334) = 3.777777781

Calculate the square root of the right side: 1.943650632

Break this problem into two subproblems by setting 
(w + 2.333333334) equal to 1.943650632 and -1.943650632.


Subproblem 1
w + 2.333333334 = 1.943650632

Simplifying
w + 2.333333334 = 1.943650632

Reorder the terms:
2.333333334 + w = 1.943650632

Solving
2.333333334 + w = 1.943650632

Solving for variable 'w'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + w = 1.943650632 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + w = 1.943650632 + -2.333333334
w = 1.943650632 + -2.333333334

Combine like terms: 1.943650632 + -2.333333334 = -0.389682702
w = -0.389682702

Simplifying
w = -0.389682702


Subproblem 2
w + 2.333333334 = -1.943650632

Simplifying
w + 2.333333334 = -1.943650632

Reorder the terms:
2.333333334 + w = -1.943650632

Solving
2.333333334 + w = -1.943650632

Solving for variable 'w'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + w = -1.943650632 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + w = -1.943650632 + -2.333333334
w = -1.943650632 + -2.333333334

Combine like terms: -1.943650632 + -2.333333334 = -4.276983966
w = -4.276983966

Simplifying
w = -4.276983966


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-0.389682702, -4.276983966}
Solution
w = {-0.389682702, -4.276983966}

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