5(v+1)-7=3(v-1)2v

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Solution for 5(v+1)-7=3(v-1)2v equation:


Simplifying
5(v + 1) + -7 = 3(v + -1) * 2v

Reorder the terms:
5(1 + v) + -7 = 3(v + -1) * 2v
(1 * 5 + v * 5) + -7 = 3(v + -1) * 2v
(5 + 5v) + -7 = 3(v + -1) * 2v

Reorder the terms:
5 + -7 + 5v = 3(v + -1) * 2v

Combine like terms: 5 + -7 = -2
-2 + 5v = 3(v + -1) * 2v

Reorder the terms:
-2 + 5v = 3(-1 + v) * 2v

Reorder the terms for easier multiplication:
-2 + 5v = 3 * 2v(-1 + v)

Multiply 3 * 2
-2 + 5v = 6v(-1 + v)
-2 + 5v = (-1 * 6v + v * 6v)
-2 + 5v = (-6v + 6v2)

Solving
-2 + 5v = -6v + 6v2

Solving for variable 'v'.

Combine like terms: 5v + 6v = 11v
-2 + 11v + -6v2 = -6v + 6v2 + 6v + -6v2

Reorder the terms:
-2 + 11v + -6v2 = -6v + 6v + 6v2 + -6v2

Combine like terms: -6v + 6v = 0
-2 + 11v + -6v2 = 0 + 6v2 + -6v2
-2 + 11v + -6v2 = 6v2 + -6v2

Combine like terms: 6v2 + -6v2 = 0
-2 + 11v + -6v2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
0.3333333333 + -1.833333333v + v2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -1.833333333v + -0.3333333333 + v2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -1.833333333v + v2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -1.833333333v + v2 = 0 + -0.3333333333
-1.833333333v + v2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-1.833333333v + v2 = -0.3333333333

The v term is -1.833333333v.  Take half its coefficient (-0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
-1.833333333v + 0.8402777775 + v2 = -0.3333333333 + 0.8402777775

Reorder the terms:
0.8402777775 + -1.833333333v + v2 = -0.3333333333 + 0.8402777775

Combine like terms: -0.3333333333 + 0.8402777775 = 0.5069444442
0.8402777775 + -1.833333333v + v2 = 0.5069444442

Factor a perfect square on the left side:
(v + -0.9166666665)(v + -0.9166666665) = 0.5069444442

Calculate the square root of the right side: 0.712000312

Break this problem into two subproblems by setting 
(v + -0.9166666665) equal to 0.712000312 and -0.712000312.

Subproblem 1

v + -0.9166666665 = 0.712000312 Simplifying v + -0.9166666665 = 0.712000312 Reorder the terms: -0.9166666665 + v = 0.712000312 Solving -0.9166666665 + v = 0.712000312 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + v = 0.712000312 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + v = 0.712000312 + 0.9166666665 v = 0.712000312 + 0.9166666665 Combine like terms: 0.712000312 + 0.9166666665 = 1.6286669785 v = 1.6286669785 Simplifying v = 1.6286669785

Subproblem 2

v + -0.9166666665 = -0.712000312 Simplifying v + -0.9166666665 = -0.712000312 Reorder the terms: -0.9166666665 + v = -0.712000312 Solving -0.9166666665 + v = -0.712000312 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + v = -0.712000312 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + v = -0.712000312 + 0.9166666665 v = -0.712000312 + 0.9166666665 Combine like terms: -0.712000312 + 0.9166666665 = 0.2046663545 v = 0.2046663545 Simplifying v = 0.2046663545

Solution

The solution to the problem is based on the solutions from the subproblems. v = {1.6286669785, 0.2046663545}

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