37w^2-312w-192924=0

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Solution for 37w^2-312w-192924=0 equation:


Simplifying
37w2 + -312w + -192924 = 0

Reorder the terms:
-192924 + -312w + 37w2 = 0

Solving
-192924 + -312w + 37w2 = 0

Solving for variable 'w'.

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

Divide each side by '37'.
-5214.162162 + -8.432432432w + w2 = 0

Move the constant term to the right:

Add '5214.162162' to each side of the equation.
-5214.162162 + -8.432432432w + 5214.162162 + w2 = 0 + 5214.162162

Reorder the terms:
-5214.162162 + 5214.162162 + -8.432432432w + w2 = 0 + 5214.162162

Combine like terms: -5214.162162 + 5214.162162 = 0.000000
0.000000 + -8.432432432w + w2 = 0 + 5214.162162
-8.432432432w + w2 = 0 + 5214.162162

Combine like terms: 0 + 5214.162162 = 5214.162162
-8.432432432w + w2 = 5214.162162

The w term is -8.432432432w.  Take half its coefficient (-4.216216216).
Square it (17.77647918) and add it to both sides.

Add '17.77647918' to each side of the equation.
-8.432432432w + 17.77647918 + w2 = 5214.162162 + 17.77647918

Reorder the terms:
17.77647918 + -8.432432432w + w2 = 5214.162162 + 17.77647918

Combine like terms: 5214.162162 + 17.77647918 = 5231.93864118
17.77647918 + -8.432432432w + w2 = 5231.93864118

Factor a perfect square on the left side:
(w + -4.216216216)(w + -4.216216216) = 5231.93864118

Calculate the square root of the right side: 72.332141135

Break this problem into two subproblems by setting 
(w + -4.216216216) equal to 72.332141135 and -72.332141135.

Subproblem 1

w + -4.216216216 = 72.332141135 Simplifying w + -4.216216216 = 72.332141135 Reorder the terms: -4.216216216 + w = 72.332141135 Solving -4.216216216 + w = 72.332141135 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4.216216216' to each side of the equation. -4.216216216 + 4.216216216 + w = 72.332141135 + 4.216216216 Combine like terms: -4.216216216 + 4.216216216 = 0.000000000 0.000000000 + w = 72.332141135 + 4.216216216 w = 72.332141135 + 4.216216216 Combine like terms: 72.332141135 + 4.216216216 = 76.548357351 w = 76.548357351 Simplifying w = 76.548357351

Subproblem 2

w + -4.216216216 = -72.332141135 Simplifying w + -4.216216216 = -72.332141135 Reorder the terms: -4.216216216 + w = -72.332141135 Solving -4.216216216 + w = -72.332141135 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4.216216216' to each side of the equation. -4.216216216 + 4.216216216 + w = -72.332141135 + 4.216216216 Combine like terms: -4.216216216 + 4.216216216 = 0.000000000 0.000000000 + w = -72.332141135 + 4.216216216 w = -72.332141135 + 4.216216216 Combine like terms: -72.332141135 + 4.216216216 = -68.115924919 w = -68.115924919 Simplifying w = -68.115924919

Solution

The solution to the problem is based on the solutions from the subproblems. w = {76.548357351, -68.115924919}

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