3w^2-20w-25=0

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Solution for 3w^2-20w-25=0 equation: 


Simplifying
3w2 + -20w + -25 = 0

Reorder the terms:
-25 + -20w + 3w2 = 0

Solving
-25 + -20w + 3w2 = 0

Solving for variable 'w'.

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

Divide each side by '3'.
-8.333333333 + -6.666666667w + w2 = 0

Move the constant term to the right:

Add '8.333333333' to each side of the equation.
-8.333333333 + -6.666666667w + 8.333333333 + w2 = 0 + 8.333333333

Reorder the terms:
-8.333333333 + 8.333333333 + -6.666666667w + w2 = 0 + 8.333333333

Combine like terms: -8.333333333 + 8.333333333 = 0.000000000
0.000000000 + -6.666666667w + w2 = 0 + 8.333333333
-6.666666667w + w2 = 0 + 8.333333333

Combine like terms: 0 + 8.333333333 = 8.333333333
-6.666666667w + w2 = 8.333333333

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 = 8.333333333 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667w + w2 = 8.333333333 + 11.11111112

Combine like terms: 8.333333333 + 11.11111112 = 19.444444453
11.11111112 + -6.666666667w + w2 = 19.444444453

Factor a perfect square on the left side:
(w + -3.333333334)(w + -3.333333334) = 19.444444453

Calculate the square root of the right side: 4.409585519

Break this problem into two subproblems by setting 
(w + -3.333333334) equal to 4.409585519 and -4.409585519.


Subproblem 1
w + -3.333333334 = 4.409585519

Simplifying
w + -3.333333334 = 4.409585519

Reorder the terms:
-3.333333334 + w = 4.409585519

Solving
-3.333333334 + w = 4.409585519

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 = 4.409585519 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + w = 4.409585519 + 3.333333334
w = 4.409585519 + 3.333333334

Combine like terms: 4.409585519 + 3.333333334 = 7.742918853
w = 7.742918853

Simplifying
w = 7.742918853


Subproblem 2
w + -3.333333334 = -4.409585519

Simplifying
w + -3.333333334 = -4.409585519

Reorder the terms:
-3.333333334 + w = -4.409585519

Solving
-3.333333334 + w = -4.409585519

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 = -4.409585519 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + w = -4.409585519 + 3.333333334
w = -4.409585519 + 3.333333334

Combine like terms: -4.409585519 + 3.333333334 = -1.076252185
w = -1.076252185

Simplifying
w = -1.076252185


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {7.742918853, -1.076252185}

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