6w^2-22w-35=0

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Solution for 6w^2-22w-35=0 equation: 


Simplifying
6w2 + -22w + -35 = 0

Reorder the terms:
-35 + -22w + 6w2 = 0

Solving
-35 + -22w + 6w2 = 0

Solving for variable 'w'.

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

Divide each side by '6'.
-5.833333333 + -3.666666667w + w2 = 0

Move the constant term to the right:

Add '5.833333333' to each side of the equation.
-5.833333333 + -3.666666667w + 5.833333333 + w2 = 0 + 5.833333333

Reorder the terms:
-5.833333333 + 5.833333333 + -3.666666667w + w2 = 0 + 5.833333333

Combine like terms: -5.833333333 + 5.833333333 = 0.000000000
0.000000000 + -3.666666667w + w2 = 0 + 5.833333333
-3.666666667w + w2 = 0 + 5.833333333

Combine like terms: 0 + 5.833333333 = 5.833333333
-3.666666667w + w2 = 5.833333333

The w term is -3.666666667w.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667w + 3.361111114 + w2 = 5.833333333 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667w + w2 = 5.833333333 + 3.361111114

Combine like terms: 5.833333333 + 3.361111114 = 9.194444447
3.361111114 + -3.666666667w + w2 = 9.194444447

Factor a perfect square on the left side:
(w + -1.833333334)(w + -1.833333334) = 9.194444447

Calculate the square root of the right side: 3.032234234

Break this problem into two subproblems by setting 
(w + -1.833333334) equal to 3.032234234 and -3.032234234.


Subproblem 1
w + -1.833333334 = 3.032234234

Simplifying
w + -1.833333334 = 3.032234234

Reorder the terms:
-1.833333334 + w = 3.032234234

Solving
-1.833333334 + w = 3.032234234

Solving for variable 'w'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + w = 3.032234234 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + w = 3.032234234 + 1.833333334
w = 3.032234234 + 1.833333334

Combine like terms: 3.032234234 + 1.833333334 = 4.865567568
w = 4.865567568

Simplifying
w = 4.865567568


Subproblem 2
w + -1.833333334 = -3.032234234

Simplifying
w + -1.833333334 = -3.032234234

Reorder the terms:
-1.833333334 + w = -3.032234234

Solving
-1.833333334 + w = -3.032234234

Solving for variable 'w'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + w = -3.032234234 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + w = -3.032234234 + 1.833333334
w = -3.032234234 + 1.833333334

Combine like terms: -3.032234234 + 1.833333334 = -1.1989009
w = -1.1989009

Simplifying
w = -1.1989009


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {4.865567568, -1.1989009}

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