3w^2+70w-74=0

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Solution for 3w^2+70w-74=0 equation:


Simplifying
3w2 + 70w + -74 = 0

Reorder the terms:
-74 + 70w + 3w2 = 0

Solving
-74 + 70w + 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'.
-24.66666667 + 23.33333333w + w2 = 0

Move the constant term to the right:

Add '24.66666667' to each side of the equation.
-24.66666667 + 23.33333333w + 24.66666667 + w2 = 0 + 24.66666667

Reorder the terms:
-24.66666667 + 24.66666667 + 23.33333333w + w2 = 0 + 24.66666667

Combine like terms: -24.66666667 + 24.66666667 = 0.00000000
0.00000000 + 23.33333333w + w2 = 0 + 24.66666667
23.33333333w + w2 = 0 + 24.66666667

Combine like terms: 0 + 24.66666667 = 24.66666667
23.33333333w + w2 = 24.66666667

The w term is 23.33333333w.  Take half its coefficient (11.66666667).
Square it (136.1111112) and add it to both sides.

Add '136.1111112' to each side of the equation.
23.33333333w + 136.1111112 + w2 = 24.66666667 + 136.1111112

Reorder the terms:
136.1111112 + 23.33333333w + w2 = 24.66666667 + 136.1111112

Combine like terms: 24.66666667 + 136.1111112 = 160.77777787
136.1111112 + 23.33333333w + w2 = 160.77777787

Factor a perfect square on the left side:
(w + 11.66666667)(w + 11.66666667) = 160.77777787

Calculate the square root of the right side: 12.679817738

Break this problem into two subproblems by setting 
(w + 11.66666667) equal to 12.679817738 and -12.679817738.

Subproblem 1

w + 11.66666667 = 12.679817738 Simplifying w + 11.66666667 = 12.679817738 Reorder the terms: 11.66666667 + w = 12.679817738 Solving 11.66666667 + w = 12.679817738 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-11.66666667' to each side of the equation. 11.66666667 + -11.66666667 + w = 12.679817738 + -11.66666667 Combine like terms: 11.66666667 + -11.66666667 = 0.00000000 0.00000000 + w = 12.679817738 + -11.66666667 w = 12.679817738 + -11.66666667 Combine like terms: 12.679817738 + -11.66666667 = 1.013151068 w = 1.013151068 Simplifying w = 1.013151068

Subproblem 2

w + 11.66666667 = -12.679817738 Simplifying w + 11.66666667 = -12.679817738 Reorder the terms: 11.66666667 + w = -12.679817738 Solving 11.66666667 + w = -12.679817738 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-11.66666667' to each side of the equation. 11.66666667 + -11.66666667 + w = -12.679817738 + -11.66666667 Combine like terms: 11.66666667 + -11.66666667 = 0.00000000 0.00000000 + w = -12.679817738 + -11.66666667 w = -12.679817738 + -11.66666667 Combine like terms: -12.679817738 + -11.66666667 = -24.346484408 w = -24.346484408 Simplifying w = -24.346484408

Solution

The solution to the problem is based on the solutions from the subproblems. w = {1.013151068, -24.346484408}

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