0.000185t^2-0.009t+0.0613=0

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Solution for 0.000185t^2-0.009t+0.0613=0 equation: 


Simplifying
0.000185t2 + -0.009t + 0.0613 = 0

Reorder the terms:
0.0613 + -0.009t + 0.000185t2 = 0

Solving
0.0613 + -0.009t + 0.000185t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
0.000185 the coefficient of the squared term: 

Divide each side by '0.000185'.
331.3513514 + -48.64864865t + t2 = 0

Move the constant term to the right:

Add '-331.3513514' to each side of the equation.
331.3513514 + -48.64864865t + -331.3513514 + t2 = 0 + -331.3513514

Reorder the terms:
331.3513514 + -331.3513514 + -48.64864865t + t2 = 0 + -331.3513514

Combine like terms: 331.3513514 + -331.3513514 = 0.0000000
0.0000000 + -48.64864865t + t2 = 0 + -331.3513514
-48.64864865t + t2 = 0 + -331.3513514

Combine like terms: 0 + -331.3513514 = -331.3513514
-48.64864865t + t2 = -331.3513514

The t term is -48.64864865t.  Take half its coefficient (-24.32432433).
Square it (591.6727541) and add it to both sides.

Add '591.6727541' to each side of the equation.
-48.64864865t + 591.6727541 + t2 = -331.3513514 + 591.6727541

Reorder the terms:
591.6727541 + -48.64864865t + t2 = -331.3513514 + 591.6727541

Combine like terms: -331.3513514 + 591.6727541 = 260.3214027
591.6727541 + -48.64864865t + t2 = 260.3214027

Factor a perfect square on the left side:
(t + -24.32432433)(t + -24.32432433) = 260.3214027

Calculate the square root of the right side: 16.134478693

Break this problem into two subproblems by setting 
(t + -24.32432433) equal to 16.134478693 and -16.134478693.


Subproblem 1
t + -24.32432433 = 16.134478693

Simplifying
t + -24.32432433 = 16.134478693

Reorder the terms:
-24.32432433 + t = 16.134478693

Solving
-24.32432433 + t = 16.134478693

Solving for variable 't'.

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

Add '24.32432433' to each side of the equation.
-24.32432433 + 24.32432433 + t = 16.134478693 + 24.32432433

Combine like terms: -24.32432433 + 24.32432433 = 0.00000000
0.00000000 + t = 16.134478693 + 24.32432433
t = 16.134478693 + 24.32432433

Combine like terms: 16.134478693 + 24.32432433 = 40.458803023
t = 40.458803023

Simplifying
t = 40.458803023


Subproblem 2
t + -24.32432433 = -16.134478693

Simplifying
t + -24.32432433 = -16.134478693

Reorder the terms:
-24.32432433 + t = -16.134478693

Solving
-24.32432433 + t = -16.134478693

Solving for variable 't'.

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

Add '24.32432433' to each side of the equation.
-24.32432433 + 24.32432433 + t = -16.134478693 + 24.32432433

Combine like terms: -24.32432433 + 24.32432433 = 0.00000000
0.00000000 + t = -16.134478693 + 24.32432433
t = -16.134478693 + 24.32432433

Combine like terms: -16.134478693 + 24.32432433 = 8.189845637
t = 8.189845637

Simplifying
t = 8.189845637


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {40.458803023, 8.189845637}

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