-5v^2+39v-40=

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Solution for -5v^2+39v-40= equation:


Simplifying
-5v2 + 39v + -40 = 0

Reorder the terms:
-40 + 39v + -5v2 = 0

Solving
-40 + 39v + -5v2 = 0

Solving for variable 'v'.

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
8 + -7.8v + v2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -7.8v + -8 + v2 = 0 + -8

Reorder the terms:
8 + -8 + -7.8v + v2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7.8v + v2 = 0 + -8
-7.8v + v2 = 0 + -8

Combine like terms: 0 + -8 = -8
-7.8v + v2 = -8

The v term is -7.8v.  Take half its coefficient (-3.9).
Square it (15.21) and add it to both sides.

Add '15.21' to each side of the equation.
-7.8v + 15.21 + v2 = -8 + 15.21

Reorder the terms:
15.21 + -7.8v + v2 = -8 + 15.21

Combine like terms: -8 + 15.21 = 7.21
15.21 + -7.8v + v2 = 7.21

Factor a perfect square on the left side:
(v + -3.9)(v + -3.9) = 7.21

Calculate the square root of the right side: 2.685144316

Break this problem into two subproblems by setting 
(v + -3.9) equal to 2.685144316 and -2.685144316.

Subproblem 1

v + -3.9 = 2.685144316 Simplifying v + -3.9 = 2.685144316 Reorder the terms: -3.9 + v = 2.685144316 Solving -3.9 + v = 2.685144316 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.9' to each side of the equation. -3.9 + 3.9 + v = 2.685144316 + 3.9 Combine like terms: -3.9 + 3.9 = 0.0 0.0 + v = 2.685144316 + 3.9 v = 2.685144316 + 3.9 Combine like terms: 2.685144316 + 3.9 = 6.585144316 v = 6.585144316 Simplifying v = 6.585144316

Subproblem 2

v + -3.9 = -2.685144316 Simplifying v + -3.9 = -2.685144316 Reorder the terms: -3.9 + v = -2.685144316 Solving -3.9 + v = -2.685144316 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.9' to each side of the equation. -3.9 + 3.9 + v = -2.685144316 + 3.9 Combine like terms: -3.9 + 3.9 = 0.0 0.0 + v = -2.685144316 + 3.9 v = -2.685144316 + 3.9 Combine like terms: -2.685144316 + 3.9 = 1.214855684 v = 1.214855684 Simplifying v = 1.214855684

Solution

The solution to the problem is based on the solutions from the subproblems. v = {6.585144316, 1.214855684}

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