t^2-22t+90.75=

Solution for t^2-22t+90.75= equation:

Simplifying
t2 + -22t + 90.75 = 0

Reorder the terms:
90.75 + -22t + t2 = 0

Solving
90.75 + -22t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-90.75' to each side of the equation.
90.75 + -22t + -90.75 + t2 = 0 + -90.75

Reorder the terms:
90.75 + -90.75 + -22t + t2 = 0 + -90.75

Combine like terms: 90.75 + -90.75 = 0.00
0.00 + -22t + t2 = 0 + -90.75
-22t + t2 = 0 + -90.75

Combine like terms: 0 + -90.75 = -90.75
-22t + t2 = -90.75

The t term is -22t.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22t + 121 + t2 = -90.75 + 121

Reorder the terms:
121 + -22t + t2 = -90.75 + 121

Combine like terms: -90.75 + 121 = 30.25
121 + -22t + t2 = 30.25

Factor a perfect square on the left side:
(t + -11)(t + -11) = 30.25

Calculate the square root of the right side: 5.5

Break this problem into two subproblems by setting 
(t + -11) equal to 5.5 and -5.5.

Subproblem 1
t + -11 = 5.5

Simplifying
t + -11 = 5.5

Reorder the terms:
-11 + t = 5.5

Solving
-11 + t = 5.5

Solving for variable 't'.

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

Add '11' to each side of the equation.
-11 + 11 + t = 5.5 + 11

Combine like terms: -11 + 11 = 0
0 + t = 5.5 + 11
t = 5.5 + 11

Combine like terms: 5.5 + 11 = 16.5
t = 16.5

Simplifying
t = 16.5

Subproblem 2
t + -11 = -5.5

Simplifying
t + -11 = -5.5

Reorder the terms:
-11 + t = -5.5

Solving
-11 + t = -5.5

Solving for variable 't'.

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

Add '11' to each side of the equation.
-11 + 11 + t = -5.5 + 11

Combine like terms: -11 + 11 = 0
0 + t = -5.5 + 11
t = -5.5 + 11

Combine like terms: -5.5 + 11 = 5.5
t = 5.5

Simplifying
t = 5.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {16.5, 5.5}