183t-16t^2=95

Solution for 183t-16t^2=95 equation:

Simplifying
183t + -16t2 = 95

Solving
183t + -16t2 = 95

Solving for variable 't'.

Reorder the terms:
-95 + 183t + -16t2 = 95 + -95

Combine like terms: 95 + -95 = 0
-95 + 183t + -16t2 = 0

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
5.9375 + -11.4375t + t2 = 0

Move the constant term to the right:

Add '-5.9375' to each side of the equation.
5.9375 + -11.4375t + -5.9375 + t2 = 0 + -5.9375

Reorder the terms:
5.9375 + -5.9375 + -11.4375t + t2 = 0 + -5.9375

Combine like terms: 5.9375 + -5.9375 = 0.0000
0.0000 + -11.4375t + t2 = 0 + -5.9375
-11.4375t + t2 = 0 + -5.9375

Combine like terms: 0 + -5.9375 = -5.9375
-11.4375t + t2 = -5.9375

The t term is -11.4375t.  Take half its coefficient (-5.71875).
Square it (32.70410156) and add it to both sides.

Add '32.70410156' to each side of the equation.
-11.4375t + 32.70410156 + t2 = -5.9375 + 32.70410156

Reorder the terms:
32.70410156 + -11.4375t + t2 = -5.9375 + 32.70410156

Combine like terms: -5.9375 + 32.70410156 = 26.76660156
32.70410156 + -11.4375t + t2 = 26.76660156

Factor a perfect square on the left side:
(t + -5.71875)(t + -5.71875) = 26.76660156

Calculate the square root of the right side: 5.173644901

Break this problem into two subproblems by setting 
(t + -5.71875) equal to 5.173644901 and -5.173644901.

Subproblem 1
t + -5.71875 = 5.173644901

Simplifying
t + -5.71875 = 5.173644901

Reorder the terms:
-5.71875 + t = 5.173644901

Solving
-5.71875 + t = 5.173644901

Solving for variable 't'.

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

Add '5.71875' to each side of the equation.
-5.71875 + 5.71875 + t = 5.173644901 + 5.71875

Combine like terms: -5.71875 + 5.71875 = 0.00000
0.00000 + t = 5.173644901 + 5.71875
t = 5.173644901 + 5.71875

Combine like terms: 5.173644901 + 5.71875 = 10.892394901
t = 10.892394901

Simplifying
t = 10.892394901

Subproblem 2
t + -5.71875 = -5.173644901

Simplifying
t + -5.71875 = -5.173644901

Reorder the terms:
-5.71875 + t = -5.173644901

Solving
-5.71875 + t = -5.173644901

Solving for variable 't'.

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

Add '5.71875' to each side of the equation.
-5.71875 + 5.71875 + t = -5.173644901 + 5.71875

Combine like terms: -5.71875 + 5.71875 = 0.00000
0.00000 + t = -5.173644901 + 5.71875
t = -5.173644901 + 5.71875

Combine like terms: -5.173644901 + 5.71875 = 0.545105099
t = 0.545105099

Simplifying
t = 0.545105099

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {10.892394901, 0.545105099}