26=-.0088v^2+.75v+14

Solution for 26=-.0088v^2+.75v+14 equation:

Simplifying
26 = -0.0088v2 + 0.75v + 14

Reorder the terms:
26 = 14 + 0.75v + -0.0088v2

Solving
26 = 14 + 0.75v + -0.0088v2

Solving for variable 'v'.

Combine like terms: 26 + -14 = 12
12 + -0.75v + 0.0088v2 = 14 + 0.75v + -0.0088v2 + -14 + -0.75v + 0.0088v2

Reorder the terms:
12 + -0.75v + 0.0088v2 = 14 + -14 + 0.75v + -0.75v + -0.0088v2 + 0.0088v2

Combine like terms: 14 + -14 = 0
12 + -0.75v + 0.0088v2 = 0 + 0.75v + -0.75v + -0.0088v2 + 0.0088v2
12 + -0.75v + 0.0088v2 = 0.75v + -0.75v + -0.0088v2 + 0.0088v2

Combine like terms: 0.75v + -0.75v = 0.00
12 + -0.75v + 0.0088v2 = 0.00 + -0.0088v2 + 0.0088v2
12 + -0.75v + 0.0088v2 = -0.0088v2 + 0.0088v2

Combine like terms: -0.0088v2 + 0.0088v2 = 0.0000
12 + -0.75v + 0.0088v2 = 0.0000

Begin completing the square.  Divide all terms by
0.0088 the coefficient of the squared term: 

Divide each side by '0.0088'.
1363.636364 + -85.22727273v + v2 = 0

Move the constant term to the right:

Add '-1363.636364' to each side of the equation.
1363.636364 + -85.22727273v + -1363.636364 + v2 = 0 + -1363.636364

Reorder the terms:
1363.636364 + -1363.636364 + -85.22727273v + v2 = 0 + -1363.636364

Combine like terms: 1363.636364 + -1363.636364 = 0.000000
0.000000 + -85.22727273v + v2 = 0 + -1363.636364
-85.22727273v + v2 = 0 + -1363.636364

Combine like terms: 0 + -1363.636364 = -1363.636364
-85.22727273v + v2 = -1363.636364

The v term is -85.22727273v.  Take half its coefficient (-42.61363637).
Square it (1815.922005) and add it to both sides.

Add '1815.922005' to each side of the equation.
-85.22727273v + 1815.922005 + v2 = -1363.636364 + 1815.922005

Reorder the terms:
1815.922005 + -85.22727273v + v2 = -1363.636364 + 1815.922005

Combine like terms: -1363.636364 + 1815.922005 = 452.285641
1815.922005 + -85.22727273v + v2 = 452.285641

Factor a perfect square on the left side:
(v + -42.61363637)(v + -42.61363637) = 452.285641

Calculate the square root of the right side: 21.267008276

Break this problem into two subproblems by setting 
(v + -42.61363637) equal to 21.267008276 and -21.267008276.

Subproblem 1
v + -42.61363637 = 21.267008276

Simplifying
v + -42.61363637 = 21.267008276

Reorder the terms:
-42.61363637 + v = 21.267008276

Solving
-42.61363637 + v = 21.267008276

Solving for variable 'v'.

Move all terms containing v to the left, all other terms to the right.

Add '42.61363637' to each side of the equation.
-42.61363637 + 42.61363637 + v = 21.267008276 + 42.61363637

Combine like terms: -42.61363637 + 42.61363637 = 0.00000000
0.00000000 + v = 21.267008276 + 42.61363637
v = 21.267008276 + 42.61363637

Combine like terms: 21.267008276 + 42.61363637 = 63.880644646
v = 63.880644646

Simplifying
v = 63.880644646

Subproblem 2
v + -42.61363637 = -21.267008276

Simplifying
v + -42.61363637 = -21.267008276

Reorder the terms:
-42.61363637 + v = -21.267008276

Solving
-42.61363637 + v = -21.267008276

Solving for variable 'v'.

Move all terms containing v to the left, all other terms to the right.

Add '42.61363637' to each side of the equation.
-42.61363637 + 42.61363637 + v = -21.267008276 + 42.61363637

Combine like terms: -42.61363637 + 42.61363637 = 0.00000000
0.00000000 + v = -21.267008276 + 42.61363637
v = -21.267008276 + 42.61363637

Combine like terms: -21.267008276 + 42.61363637 = 21.346628094
v = 21.346628094

Simplifying
v = 21.346628094

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {63.880644646, 21.346628094}