v^2+3v-38=

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Solution for v^2+3v-38= equation:


Simplifying
v2 + 3v + -38 = 0

Reorder the terms:
-38 + 3v + v2 = 0

Solving
-38 + 3v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '38' to each side of the equation.
-38 + 3v + 38 + v2 = 0 + 38

Reorder the terms:
-38 + 38 + 3v + v2 = 0 + 38

Combine like terms: -38 + 38 = 0
0 + 3v + v2 = 0 + 38
3v + v2 = 0 + 38

Combine like terms: 0 + 38 = 38
3v + v2 = 38

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 = 38 + 2.25

Reorder the terms:
2.25 + 3v + v2 = 38 + 2.25

Combine like terms: 38 + 2.25 = 40.25
2.25 + 3v + v2 = 40.25

Factor a perfect square on the left side:
(v + 1.5)(v + 1.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(v + 1.5) equal to 6.34428877 and -6.34428877.

Subproblem 1

v + 1.5 = 6.34428877 Simplifying v + 1.5 = 6.34428877 Reorder the terms: 1.5 + v = 6.34428877 Solving 1.5 + v = 6.34428877 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 = 6.34428877 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + v = 6.34428877 + -1.5 v = 6.34428877 + -1.5 Combine like terms: 6.34428877 + -1.5 = 4.84428877 v = 4.84428877 Simplifying v = 4.84428877

Subproblem 2

v + 1.5 = -6.34428877 Simplifying v + 1.5 = -6.34428877 Reorder the terms: 1.5 + v = -6.34428877 Solving 1.5 + v = -6.34428877 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 = -6.34428877 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + v = -6.34428877 + -1.5 v = -6.34428877 + -1.5 Combine like terms: -6.34428877 + -1.5 = -7.84428877 v = -7.84428877 Simplifying v = -7.84428877

Solution

The solution to the problem is based on the solutions from the subproblems. v = {4.84428877, -7.84428877}

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