9(2+w)4w=3w-10

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Solution for 9(2+w)4w=3w-10 equation:


Simplifying
9(2 + w) * 4w = 3w + -10

Reorder the terms for easier multiplication:
9 * 4w(2 + w) = 3w + -10

Multiply 9 * 4
36w(2 + w) = 3w + -10
(2 * 36w + w * 36w) = 3w + -10
(72w + 36w2) = 3w + -10

Reorder the terms:
72w + 36w2 = -10 + 3w

Solving
72w + 36w2 = -10 + 3w

Solving for variable 'w'.

Reorder the terms:
10 + 72w + -3w + 36w2 = -10 + 3w + 10 + -3w

Combine like terms: 72w + -3w = 69w
10 + 69w + 36w2 = -10 + 3w + 10 + -3w

Reorder the terms:
10 + 69w + 36w2 = -10 + 10 + 3w + -3w

Combine like terms: -10 + 10 = 0
10 + 69w + 36w2 = 0 + 3w + -3w
10 + 69w + 36w2 = 3w + -3w

Combine like terms: 3w + -3w = 0
10 + 69w + 36w2 = 0

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

Divide each side by '36'.
0.2777777778 + 1.916666667w + w2 = 0

Move the constant term to the right:

Add '-0.2777777778' to each side of the equation.
0.2777777778 + 1.916666667w + -0.2777777778 + w2 = 0 + -0.2777777778

Reorder the terms:
0.2777777778 + -0.2777777778 + 1.916666667w + w2 = 0 + -0.2777777778

Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000
0.0000000000 + 1.916666667w + w2 = 0 + -0.2777777778
1.916666667w + w2 = 0 + -0.2777777778

Combine like terms: 0 + -0.2777777778 = -0.2777777778
1.916666667w + w2 = -0.2777777778

The w term is 1.916666667w.  Take half its coefficient (0.9583333335).
Square it (0.9184027781) and add it to both sides.

Add '0.9184027781' to each side of the equation.
1.916666667w + 0.9184027781 + w2 = -0.2777777778 + 0.9184027781

Reorder the terms:
0.9184027781 + 1.916666667w + w2 = -0.2777777778 + 0.9184027781

Combine like terms: -0.2777777778 + 0.9184027781 = 0.6406250003
0.9184027781 + 1.916666667w + w2 = 0.6406250003

Factor a perfect square on the left side:
(w + 0.9583333335)(w + 0.9583333335) = 0.6406250003

Calculate the square root of the right side: 0.80039053

Break this problem into two subproblems by setting 
(w + 0.9583333335) equal to 0.80039053 and -0.80039053.

Subproblem 1

w + 0.9583333335 = 0.80039053 Simplifying w + 0.9583333335 = 0.80039053 Reorder the terms: 0.9583333335 + w = 0.80039053 Solving 0.9583333335 + w = 0.80039053 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.9583333335' to each side of the equation. 0.9583333335 + -0.9583333335 + w = 0.80039053 + -0.9583333335 Combine like terms: 0.9583333335 + -0.9583333335 = 0.0000000000 0.0000000000 + w = 0.80039053 + -0.9583333335 w = 0.80039053 + -0.9583333335 Combine like terms: 0.80039053 + -0.9583333335 = -0.1579428035 w = -0.1579428035 Simplifying w = -0.1579428035

Subproblem 2

w + 0.9583333335 = -0.80039053 Simplifying w + 0.9583333335 = -0.80039053 Reorder the terms: 0.9583333335 + w = -0.80039053 Solving 0.9583333335 + w = -0.80039053 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.9583333335' to each side of the equation. 0.9583333335 + -0.9583333335 + w = -0.80039053 + -0.9583333335 Combine like terms: 0.9583333335 + -0.9583333335 = 0.0000000000 0.0000000000 + w = -0.80039053 + -0.9583333335 w = -0.80039053 + -0.9583333335 Combine like terms: -0.80039053 + -0.9583333335 = -1.7587238635 w = -1.7587238635 Simplifying w = -1.7587238635

Solution

The solution to the problem is based on the solutions from the subproblems. w = {-0.1579428035, -1.7587238635}

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