-9w^2+3w+50=0

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Solution for -9w^2+3w+50=0 equation:


Simplifying
-9w2 + 3w + 50 = 0

Reorder the terms:
50 + 3w + -9w2 = 0

Solving
50 + 3w + -9w2 = 0

Solving for variable 'w'.

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-5.555555556 + -0.3333333333w + w2 = 0

Move the constant term to the right:

Add '5.555555556' to each side of the equation.
-5.555555556 + -0.3333333333w + 5.555555556 + w2 = 0 + 5.555555556

Reorder the terms:
-5.555555556 + 5.555555556 + -0.3333333333w + w2 = 0 + 5.555555556

Combine like terms: -5.555555556 + 5.555555556 = 0.000000000
0.000000000 + -0.3333333333w + w2 = 0 + 5.555555556
-0.3333333333w + w2 = 0 + 5.555555556

Combine like terms: 0 + 5.555555556 = 5.555555556
-0.3333333333w + w2 = 5.555555556

The w term is -0.3333333333w.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333w + 0.02777777779 + w2 = 5.555555556 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333w + w2 = 5.555555556 + 0.02777777779

Combine like terms: 5.555555556 + 0.02777777779 = 5.58333333379
0.02777777779 + -0.3333333333w + w2 = 5.58333333379

Factor a perfect square on the left side:
(w + -0.1666666667)(w + -0.1666666667) = 5.58333333379

Calculate the square root of the right side: 2.362907813

Break this problem into two subproblems by setting 
(w + -0.1666666667) equal to 2.362907813 and -2.362907813.

Subproblem 1

w + -0.1666666667 = 2.362907813 Simplifying w + -0.1666666667 = 2.362907813 Reorder the terms: -0.1666666667 + w = 2.362907813 Solving -0.1666666667 + w = 2.362907813 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + w = 2.362907813 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + w = 2.362907813 + 0.1666666667 w = 2.362907813 + 0.1666666667 Combine like terms: 2.362907813 + 0.1666666667 = 2.5295744797 w = 2.5295744797 Simplifying w = 2.5295744797

Subproblem 2

w + -0.1666666667 = -2.362907813 Simplifying w + -0.1666666667 = -2.362907813 Reorder the terms: -0.1666666667 + w = -2.362907813 Solving -0.1666666667 + w = -2.362907813 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + w = -2.362907813 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + w = -2.362907813 + 0.1666666667 w = -2.362907813 + 0.1666666667 Combine like terms: -2.362907813 + 0.1666666667 = -2.1962411463 w = -2.1962411463 Simplifying w = -2.1962411463

Solution

The solution to the problem is based on the solutions from the subproblems. w = {2.5295744797, -2.1962411463}

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