v^2+6v-55=-3

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Solution for v^2+6v-55=-3 equation:


Simplifying
v2 + 6v + -55 = -3

Reorder the terms:
-55 + 6v + v2 = -3

Solving
-55 + 6v + v2 = -3

Solving for variable 'v'.

Reorder the terms:
-55 + 3 + 6v + v2 = -3 + 3

Combine like terms: -55 + 3 = -52
-52 + 6v + v2 = -3 + 3

Combine like terms: -3 + 3 = 0
-52 + 6v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '52' to each side of the equation.
-52 + 6v + 52 + v2 = 0 + 52

Reorder the terms:
-52 + 52 + 6v + v2 = 0 + 52

Combine like terms: -52 + 52 = 0
0 + 6v + v2 = 0 + 52
6v + v2 = 0 + 52

Combine like terms: 0 + 52 = 52
6v + v2 = 52

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 = 52 + 9

Reorder the terms:
9 + 6v + v2 = 52 + 9

Combine like terms: 52 + 9 = 61
9 + 6v + v2 = 61

Factor a perfect square on the left side:
(v + 3)(v + 3) = 61

Calculate the square root of the right side: 7.810249676

Break this problem into two subproblems by setting 
(v + 3) equal to 7.810249676 and -7.810249676.

Subproblem 1

v + 3 = 7.810249676 Simplifying v + 3 = 7.810249676 Reorder the terms: 3 + v = 7.810249676 Solving 3 + v = 7.810249676 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 = 7.810249676 + -3 Combine like terms: 3 + -3 = 0 0 + v = 7.810249676 + -3 v = 7.810249676 + -3 Combine like terms: 7.810249676 + -3 = 4.810249676 v = 4.810249676 Simplifying v = 4.810249676

Subproblem 2

v + 3 = -7.810249676 Simplifying v + 3 = -7.810249676 Reorder the terms: 3 + v = -7.810249676 Solving 3 + v = -7.810249676 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 = -7.810249676 + -3 Combine like terms: 3 + -3 = 0 0 + v = -7.810249676 + -3 v = -7.810249676 + -3 Combine like terms: -7.810249676 + -3 = -10.810249676 v = -10.810249676 Simplifying v = -10.810249676

Solution

The solution to the problem is based on the solutions from the subproblems. v = {4.810249676, -10.810249676}

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