17=-1.85t^2+20t+1

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Solution for 17=-1.85t^2+20t+1 equation:


Simplifying
17 = -1.85t2 + 20t + 1

Reorder the terms:
17 = 1 + 20t + -1.85t2

Solving
17 = 1 + 20t + -1.85t2

Solving for variable 't'.

Combine like terms: 17 + -1 = 16
16 + -20t + 1.85t2 = 1 + 20t + -1.85t2 + -1 + -20t + 1.85t2

Reorder the terms:
16 + -20t + 1.85t2 = 1 + -1 + 20t + -20t + -1.85t2 + 1.85t2

Combine like terms: 1 + -1 = 0
16 + -20t + 1.85t2 = 0 + 20t + -20t + -1.85t2 + 1.85t2
16 + -20t + 1.85t2 = 20t + -20t + -1.85t2 + 1.85t2

Combine like terms: 20t + -20t = 0
16 + -20t + 1.85t2 = 0 + -1.85t2 + 1.85t2
16 + -20t + 1.85t2 = -1.85t2 + 1.85t2

Combine like terms: -1.85t2 + 1.85t2 = 0.00
16 + -20t + 1.85t2 = 0.00

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

Divide each side by '1.85'.
8.648648649 + -10.81081081t + t2 = 0

Move the constant term to the right:

Add '-8.648648649' to each side of the equation.
8.648648649 + -10.81081081t + -8.648648649 + t2 = 0 + -8.648648649

Reorder the terms:
8.648648649 + -8.648648649 + -10.81081081t + t2 = 0 + -8.648648649

Combine like terms: 8.648648649 + -8.648648649 = 0.000000000
0.000000000 + -10.81081081t + t2 = 0 + -8.648648649
-10.81081081t + t2 = 0 + -8.648648649

Combine like terms: 0 + -8.648648649 = -8.648648649
-10.81081081t + t2 = -8.648648649

The t term is -10.81081081t.  Take half its coefficient (-5.405405405).
Square it (29.21840759) and add it to both sides.

Add '29.21840759' to each side of the equation.
-10.81081081t + 29.21840759 + t2 = -8.648648649 + 29.21840759

Reorder the terms:
29.21840759 + -10.81081081t + t2 = -8.648648649 + 29.21840759

Combine like terms: -8.648648649 + 29.21840759 = 20.569758941
29.21840759 + -10.81081081t + t2 = 20.569758941

Factor a perfect square on the left side:
(t + -5.405405405)(t + -5.405405405) = 20.569758941

Calculate the square root of the right side: 4.535389613

Break this problem into two subproblems by setting 
(t + -5.405405405) equal to 4.535389613 and -4.535389613.

Subproblem 1

t + -5.405405405 = 4.535389613 Simplifying t + -5.405405405 = 4.535389613 Reorder the terms: -5.405405405 + t = 4.535389613 Solving -5.405405405 + t = 4.535389613 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.405405405' to each side of the equation. -5.405405405 + 5.405405405 + t = 4.535389613 + 5.405405405 Combine like terms: -5.405405405 + 5.405405405 = 0.000000000 0.000000000 + t = 4.535389613 + 5.405405405 t = 4.535389613 + 5.405405405 Combine like terms: 4.535389613 + 5.405405405 = 9.940795018 t = 9.940795018 Simplifying t = 9.940795018

Subproblem 2

t + -5.405405405 = -4.535389613 Simplifying t + -5.405405405 = -4.535389613 Reorder the terms: -5.405405405 + t = -4.535389613 Solving -5.405405405 + t = -4.535389613 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.405405405' to each side of the equation. -5.405405405 + 5.405405405 + t = -4.535389613 + 5.405405405 Combine like terms: -5.405405405 + 5.405405405 = 0.000000000 0.000000000 + t = -4.535389613 + 5.405405405 t = -4.535389613 + 5.405405405 Combine like terms: -4.535389613 + 5.405405405 = 0.870015792 t = 0.870015792 Simplifying t = 0.870015792

Solution

The solution to the problem is based on the solutions from the subproblems. t = {9.940795018, 0.870015792}

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