v^2+3v-128=0

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Solution for v^2+3v-128=0 equation:


Simplifying
v2 + 3v + -128 = 0

Reorder the terms:
-128 + 3v + v2 = 0

Solving
-128 + 3v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '128' to each side of the equation.
-128 + 3v + 128 + v2 = 0 + 128

Reorder the terms:
-128 + 128 + 3v + v2 = 0 + 128

Combine like terms: -128 + 128 = 0
0 + 3v + v2 = 0 + 128
3v + v2 = 0 + 128

Combine like terms: 0 + 128 = 128
3v + v2 = 128

The v term is 3v.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3v + 2.25 + v2 = 128 + 2.25

Reorder the terms:
2.25 + 3v + v2 = 128 + 2.25

Combine like terms: 128 + 2.25 = 130.25
2.25 + 3v + v2 = 130.25

Factor a perfect square on the left side:
(v + 1.5)(v + 1.5) = 130.25

Calculate the square root of the right side: 11.412712211

Break this problem into two subproblems by setting 
(v + 1.5) equal to 11.412712211 and -11.412712211.

Subproblem 1

v + 1.5 = 11.412712211 Simplifying v + 1.5 = 11.412712211 Reorder the terms: 1.5 + v = 11.412712211 Solving 1.5 + v = 11.412712211 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + v = 11.412712211 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + v = 11.412712211 + -1.5 v = 11.412712211 + -1.5 Combine like terms: 11.412712211 + -1.5 = 9.912712211 v = 9.912712211 Simplifying v = 9.912712211

Subproblem 2

v + 1.5 = -11.412712211 Simplifying v + 1.5 = -11.412712211 Reorder the terms: 1.5 + v = -11.412712211 Solving 1.5 + v = -11.412712211 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + v = -11.412712211 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + v = -11.412712211 + -1.5 v = -11.412712211 + -1.5 Combine like terms: -11.412712211 + -1.5 = -12.912712211 v = -12.912712211 Simplifying v = -12.912712211

Solution

The solution to the problem is based on the solutions from the subproblems. v = {9.912712211, -12.912712211}

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