v^2+7.1v-62.48=0

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Solution for v^2+7.1v-62.48=0 equation:


Simplifying
v2 + 7.1v + -62.48 = 0

Reorder the terms:
-62.48 + 7.1v + v2 = 0

Solving
-62.48 + 7.1v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '62.48' to each side of the equation.
-62.48 + 7.1v + 62.48 + v2 = 0 + 62.48

Reorder the terms:
-62.48 + 62.48 + 7.1v + v2 = 0 + 62.48

Combine like terms: -62.48 + 62.48 = 0.00
0.00 + 7.1v + v2 = 0 + 62.48
7.1v + v2 = 0 + 62.48

Combine like terms: 0 + 62.48 = 62.48
7.1v + v2 = 62.48

The v term is 7.1v.  Take half its coefficient (3.55).
Square it (12.6025) and add it to both sides.

Add '12.6025' to each side of the equation.
7.1v + 12.6025 + v2 = 62.48 + 12.6025

Reorder the terms:
12.6025 + 7.1v + v2 = 62.48 + 12.6025

Combine like terms: 62.48 + 12.6025 = 75.0825
12.6025 + 7.1v + v2 = 75.0825

Factor a perfect square on the left side:
(v + 3.55)(v + 3.55) = 75.0825

Calculate the square root of the right side: 8.665015868

Break this problem into two subproblems by setting 
(v + 3.55) equal to 8.665015868 and -8.665015868.

Subproblem 1

v + 3.55 = 8.665015868 Simplifying v + 3.55 = 8.665015868 Reorder the terms: 3.55 + v = 8.665015868 Solving 3.55 + v = 8.665015868 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3.55' to each side of the equation. 3.55 + -3.55 + v = 8.665015868 + -3.55 Combine like terms: 3.55 + -3.55 = 0.00 0.00 + v = 8.665015868 + -3.55 v = 8.665015868 + -3.55 Combine like terms: 8.665015868 + -3.55 = 5.115015868 v = 5.115015868 Simplifying v = 5.115015868

Subproblem 2

v + 3.55 = -8.665015868 Simplifying v + 3.55 = -8.665015868 Reorder the terms: 3.55 + v = -8.665015868 Solving 3.55 + v = -8.665015868 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3.55' to each side of the equation. 3.55 + -3.55 + v = -8.665015868 + -3.55 Combine like terms: 3.55 + -3.55 = 0.00 0.00 + v = -8.665015868 + -3.55 v = -8.665015868 + -3.55 Combine like terms: -8.665015868 + -3.55 = -12.215015868 v = -12.215015868 Simplifying v = -12.215015868

Solution

The solution to the problem is based on the solutions from the subproblems. v = {5.115015868, -12.215015868}

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