.0765t^2-.844t+1.806=0

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Solution for .0765t^2-.844t+1.806=0 equation: 


Simplifying
0.0765t2 + -0.844t + 1.806 = 0

Reorder the terms:
1.806 + -0.844t + 0.0765t2 = 0

Solving
1.806 + -0.844t + 0.0765t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
0.0765 the coefficient of the squared term: 

Divide each side by '0.0765'.
23.60784314 + -11.03267974t + t2 = 0

Move the constant term to the right:

Add '-23.60784314' to each side of the equation.
23.60784314 + -11.03267974t + -23.60784314 + t2 = 0 + -23.60784314

Reorder the terms:
23.60784314 + -23.60784314 + -11.03267974t + t2 = 0 + -23.60784314

Combine like terms: 23.60784314 + -23.60784314 = 0.00000000
0.00000000 + -11.03267974t + t2 = 0 + -23.60784314
-11.03267974t + t2 = 0 + -23.60784314

Combine like terms: 0 + -23.60784314 = -23.60784314
-11.03267974t + t2 = -23.60784314

The t term is -11.03267974t.  Take half its coefficient (-5.51633987).
Square it (30.43000556) and add it to both sides.

Add '30.43000556' to each side of the equation.
-11.03267974t + 30.43000556 + t2 = -23.60784314 + 30.43000556

Reorder the terms:
30.43000556 + -11.03267974t + t2 = -23.60784314 + 30.43000556

Combine like terms: -23.60784314 + 30.43000556 = 6.82216242
30.43000556 + -11.03267974t + t2 = 6.82216242

Factor a perfect square on the left side:
(t + -5.51633987)(t + -5.51633987) = 6.82216242

Calculate the square root of the right side: 2.611926955

Break this problem into two subproblems by setting 
(t + -5.51633987) equal to 2.611926955 and -2.611926955.


Subproblem 1
t + -5.51633987 = 2.611926955

Simplifying
t + -5.51633987 = 2.611926955

Reorder the terms:
-5.51633987 + t = 2.611926955

Solving
-5.51633987 + t = 2.611926955

Solving for variable 't'.

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

Add '5.51633987' to each side of the equation.
-5.51633987 + 5.51633987 + t = 2.611926955 + 5.51633987

Combine like terms: -5.51633987 + 5.51633987 = 0.00000000
0.00000000 + t = 2.611926955 + 5.51633987
t = 2.611926955 + 5.51633987

Combine like terms: 2.611926955 + 5.51633987 = 8.128266825
t = 8.128266825

Simplifying
t = 8.128266825


Subproblem 2
t + -5.51633987 = -2.611926955

Simplifying
t + -5.51633987 = -2.611926955

Reorder the terms:
-5.51633987 + t = -2.611926955

Solving
-5.51633987 + t = -2.611926955

Solving for variable 't'.

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

Add '5.51633987' to each side of the equation.
-5.51633987 + 5.51633987 + t = -2.611926955 + 5.51633987

Combine like terms: -5.51633987 + 5.51633987 = 0.00000000
0.00000000 + t = -2.611926955 + 5.51633987
t = -2.611926955 + 5.51633987

Combine like terms: -2.611926955 + 5.51633987 = 2.904412915
t = 2.904412915

Simplifying
t = 2.904412915


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {8.128266825, 2.904412915}

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