-4v^2+19v-31=0

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Solution for -4v^2+19v-31=0 equation:


Simplifying
-4v2 + 19v + -31 = 0

Reorder the terms:
-31 + 19v + -4v2 = 0

Solving
-31 + 19v + -4v2 = 0

Solving for variable 'v'.

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
7.75 + -4.75v + v2 = 0

Move the constant term to the right:

Add '-7.75' to each side of the equation.
7.75 + -4.75v + -7.75 + v2 = 0 + -7.75

Reorder the terms:
7.75 + -7.75 + -4.75v + v2 = 0 + -7.75

Combine like terms: 7.75 + -7.75 = 0.00
0.00 + -4.75v + v2 = 0 + -7.75
-4.75v + v2 = 0 + -7.75

Combine like terms: 0 + -7.75 = -7.75
-4.75v + v2 = -7.75

The v term is -4.75v.  Take half its coefficient (-2.375).
Square it (5.640625) and add it to both sides.

Add '5.640625' to each side of the equation.
-4.75v + 5.640625 + v2 = -7.75 + 5.640625

Reorder the terms:
5.640625 + -4.75v + v2 = -7.75 + 5.640625

Combine like terms: -7.75 + 5.640625 = -2.109375
5.640625 + -4.75v + v2 = -2.109375

Factor a perfect square on the left side:
(v + -2.375)(v + -2.375) = -2.109375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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