2v^2-3v-8=8

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Solution for 2v^2-3v-8=8 equation:


Simplifying
2v2 + -3v + -8 = 8

Reorder the terms:
-8 + -3v + 2v2 = 8

Solving
-8 + -3v + 2v2 = 8

Solving for variable 'v'.

Reorder the terms:
-8 + -8 + -3v + 2v2 = 8 + -8

Combine like terms: -8 + -8 = -16
-16 + -3v + 2v2 = 8 + -8

Combine like terms: 8 + -8 = 0
-16 + -3v + 2v2 = 0

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

Divide each side by '2'.
-8 + -1.5v + v2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -1.5v + 8 + v2 = 0 + 8

Reorder the terms:
-8 + 8 + -1.5v + v2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1.5v + v2 = 0 + 8
-1.5v + v2 = 0 + 8

Combine like terms: 0 + 8 = 8
-1.5v + v2 = 8

The v term is -1.5v.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5v + 0.5625 + v2 = 8 + 0.5625

Reorder the terms:
0.5625 + -1.5v + v2 = 8 + 0.5625

Combine like terms: 8 + 0.5625 = 8.5625
0.5625 + -1.5v + v2 = 8.5625

Factor a perfect square on the left side:
(v + -0.75)(v + -0.75) = 8.5625

Calculate the square root of the right side: 2.926174978

Break this problem into two subproblems by setting 
(v + -0.75) equal to 2.926174978 and -2.926174978.

Subproblem 1

v + -0.75 = 2.926174978 Simplifying v + -0.75 = 2.926174978 Reorder the terms: -0.75 + v = 2.926174978 Solving -0.75 + v = 2.926174978 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + v = 2.926174978 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + v = 2.926174978 + 0.75 v = 2.926174978 + 0.75 Combine like terms: 2.926174978 + 0.75 = 3.676174978 v = 3.676174978 Simplifying v = 3.676174978

Subproblem 2

v + -0.75 = -2.926174978 Simplifying v + -0.75 = -2.926174978 Reorder the terms: -0.75 + v = -2.926174978 Solving -0.75 + v = -2.926174978 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + v = -2.926174978 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + v = -2.926174978 + 0.75 v = -2.926174978 + 0.75 Combine like terms: -2.926174978 + 0.75 = -2.176174978 v = -2.176174978 Simplifying v = -2.176174978

Solution

The solution to the problem is based on the solutions from the subproblems. v = {3.676174978, -2.176174978}

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