-2v^2-10v-4=-3v^2-4v

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Solution for -2v^2-10v-4=-3v^2-4v equation:


Simplifying
-2v2 + -10v + -4 = -3v2 + -4v

Reorder the terms:
-4 + -10v + -2v2 = -3v2 + -4v

Reorder the terms:
-4 + -10v + -2v2 = -4v + -3v2

Solving
-4 + -10v + -2v2 = -4v + -3v2

Solving for variable 'v'.

Reorder the terms:
-4 + -10v + 4v + -2v2 + 3v2 = -4v + -3v2 + 4v + 3v2

Combine like terms: -10v + 4v = -6v
-4 + -6v + -2v2 + 3v2 = -4v + -3v2 + 4v + 3v2

Combine like terms: -2v2 + 3v2 = 1v2
-4 + -6v + 1v2 = -4v + -3v2 + 4v + 3v2

Reorder the terms:
-4 + -6v + 1v2 = -4v + 4v + -3v2 + 3v2

Combine like terms: -4v + 4v = 0
-4 + -6v + 1v2 = 0 + -3v2 + 3v2
-4 + -6v + 1v2 = -3v2 + 3v2

Combine like terms: -3v2 + 3v2 = 0
-4 + -6v + 1v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -6v + 4 + v2 = 0 + 4

Reorder the terms:
-4 + 4 + -6v + v2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -6v + v2 = 0 + 4
-6v + v2 = 0 + 4

Combine like terms: 0 + 4 = 4
-6v + v2 = 4

The v term is -6v.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6v + 9 + v2 = 4 + 9

Reorder the terms:
9 + -6v + v2 = 4 + 9

Combine like terms: 4 + 9 = 13
9 + -6v + v2 = 13

Factor a perfect square on the left side:
(v + -3)(v + -3) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(v + -3) equal to 3.605551275 and -3.605551275.

Subproblem 1

v + -3 = 3.605551275 Simplifying v + -3 = 3.605551275 Reorder the terms: -3 + v = 3.605551275 Solving -3 + v = 3.605551275 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + v = 3.605551275 + 3 Combine like terms: -3 + 3 = 0 0 + v = 3.605551275 + 3 v = 3.605551275 + 3 Combine like terms: 3.605551275 + 3 = 6.605551275 v = 6.605551275 Simplifying v = 6.605551275

Subproblem 2

v + -3 = -3.605551275 Simplifying v + -3 = -3.605551275 Reorder the terms: -3 + v = -3.605551275 Solving -3 + v = -3.605551275 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + v = -3.605551275 + 3 Combine like terms: -3 + 3 = 0 0 + v = -3.605551275 + 3 v = -3.605551275 + 3 Combine like terms: -3.605551275 + 3 = -0.605551275 v = -0.605551275 Simplifying v = -0.605551275

Solution

The solution to the problem is based on the solutions from the subproblems. v = {6.605551275, -0.605551275}

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