5w^2-11w+2=2w^2+9w-5

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Solution for 5w^2-11w+2=2w^2+9w-5 equation: 


Simplifying
5w2 + -11w + 2 = 2w2 + 9w + -5

Reorder the terms:
2 + -11w + 5w2 = 2w2 + 9w + -5

Reorder the terms:
2 + -11w + 5w2 = -5 + 9w + 2w2

Solving
2 + -11w + 5w2 = -5 + 9w + 2w2

Solving for variable 'w'.

Reorder the terms:
2 + 5 + -11w + -9w + 5w2 + -2w2 = -5 + 9w + 2w2 + 5 + -9w + -2w2

Combine like terms: 2 + 5 = 7
7 + -11w + -9w + 5w2 + -2w2 = -5 + 9w + 2w2 + 5 + -9w + -2w2

Combine like terms: -11w + -9w = -20w
7 + -20w + 5w2 + -2w2 = -5 + 9w + 2w2 + 5 + -9w + -2w2

Combine like terms: 5w2 + -2w2 = 3w2
7 + -20w + 3w2 = -5 + 9w + 2w2 + 5 + -9w + -2w2

Reorder the terms:
7 + -20w + 3w2 = -5 + 5 + 9w + -9w + 2w2 + -2w2

Combine like terms: -5 + 5 = 0
7 + -20w + 3w2 = 0 + 9w + -9w + 2w2 + -2w2
7 + -20w + 3w2 = 9w + -9w + 2w2 + -2w2

Combine like terms: 9w + -9w = 0
7 + -20w + 3w2 = 0 + 2w2 + -2w2
7 + -20w + 3w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
7 + -20w + 3w2 = 0

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

Divide each side by '3'.
2.333333333 + -6.666666667w + w2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -6.666666667w + -2.333333333 + w2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -6.666666667w + w2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -6.666666667w + w2 = 0 + -2.333333333
-6.666666667w + w2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-6.666666667w + w2 = -2.333333333

The w term is -6.666666667w.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667w + 11.11111112 + w2 = -2.333333333 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667w + w2 = -2.333333333 + 11.11111112

Combine like terms: -2.333333333 + 11.11111112 = 8.777777787
11.11111112 + -6.666666667w + w2 = 8.777777787

Factor a perfect square on the left side:
(w + -3.333333334)(w + -3.333333334) = 8.777777787

Calculate the square root of the right side: 2.962731474

Break this problem into two subproblems by setting 
(w + -3.333333334) equal to 2.962731474 and -2.962731474.


Subproblem 1
w + -3.333333334 = 2.962731474

Simplifying
w + -3.333333334 = 2.962731474

Reorder the terms:
-3.333333334 + w = 2.962731474

Solving
-3.333333334 + w = 2.962731474

Solving for variable 'w'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + w = 2.962731474 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + w = 2.962731474 + 3.333333334
w = 2.962731474 + 3.333333334

Combine like terms: 2.962731474 + 3.333333334 = 6.296064808
w = 6.296064808

Simplifying
w = 6.296064808


Subproblem 2
w + -3.333333334 = -2.962731474

Simplifying
w + -3.333333334 = -2.962731474

Reorder the terms:
-3.333333334 + w = -2.962731474

Solving
-3.333333334 + w = -2.962731474

Solving for variable 'w'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + w = -2.962731474 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + w = -2.962731474 + 3.333333334
w = -2.962731474 + 3.333333334

Combine like terms: -2.962731474 + 3.333333334 = 0.37060186
w = 0.37060186

Simplifying
w = 0.37060186


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {6.296064808, 0.37060186}

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