7v^2+3v-2=0

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Solution for 7v^2+3v-2=0 equation:


Simplifying
7v2 + 3v + -2 = 0

Reorder the terms:
-2 + 3v + 7v2 = 0

Solving
-2 + 3v + 7v2 = 0

Solving for variable 'v'.

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

Divide each side by '7'.
-0.2857142857 + 0.4285714286v + v2 = 0

Move the constant term to the right:

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 0.4285714286v + 0.2857142857 + v2 = 0 + 0.2857142857

Reorder the terms:
-0.2857142857 + 0.2857142857 + 0.4285714286v + v2 = 0 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + 0.4285714286v + v2 = 0 + 0.2857142857
0.4285714286v + v2 = 0 + 0.2857142857

Combine like terms: 0 + 0.2857142857 = 0.2857142857
0.4285714286v + v2 = 0.2857142857

The v term is 0.4285714286v.  Take half its coefficient (0.2142857143).
Square it (0.04591836735) and add it to both sides.

Add '0.04591836735' to each side of the equation.
0.4285714286v + 0.04591836735 + v2 = 0.2857142857 + 0.04591836735

Reorder the terms:
0.04591836735 + 0.4285714286v + v2 = 0.2857142857 + 0.04591836735

Combine like terms: 0.2857142857 + 0.04591836735 = 0.33163265305
0.04591836735 + 0.4285714286v + v2 = 0.33163265305

Factor a perfect square on the left side:
(v + 0.2142857143)(v + 0.2142857143) = 0.33163265305

Calculate the square root of the right side: 0.575875553

Break this problem into two subproblems by setting 
(v + 0.2142857143) equal to 0.575875553 and -0.575875553.

Subproblem 1

v + 0.2142857143 = 0.575875553 Simplifying v + 0.2142857143 = 0.575875553 Reorder the terms: 0.2142857143 + v = 0.575875553 Solving 0.2142857143 + v = 0.575875553 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + v = 0.575875553 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + v = 0.575875553 + -0.2142857143 v = 0.575875553 + -0.2142857143 Combine like terms: 0.575875553 + -0.2142857143 = 0.3615898387 v = 0.3615898387 Simplifying v = 0.3615898387

Subproblem 2

v + 0.2142857143 = -0.575875553 Simplifying v + 0.2142857143 = -0.575875553 Reorder the terms: 0.2142857143 + v = -0.575875553 Solving 0.2142857143 + v = -0.575875553 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + v = -0.575875553 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + v = -0.575875553 + -0.2142857143 v = -0.575875553 + -0.2142857143 Combine like terms: -0.575875553 + -0.2142857143 = -0.7901612673 v = -0.7901612673 Simplifying v = -0.7901612673

Solution

The solution to the problem is based on the solutions from the subproblems. v = {0.3615898387, -0.7901612673}

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