65000000=4.5t^2+43.5t+17

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Solution for 65000000=4.5t^2+43.5t+17 equation: 


Simplifying
65000000 = 4.5t2 + 43.5t + 17

Reorder the terms:
65000000 = 17 + 43.5t + 4.5t2

Solving
65000000 = 17 + 43.5t + 4.5t2

Solving for variable 't'.

Combine like terms: 65000000 + -17 = 64999983
64999983 + -43.5t + -4.5t2 = 17 + 43.5t + 4.5t2 + -17 + -43.5t + -4.5t2

Reorder the terms:
64999983 + -43.5t + -4.5t2 = 17 + -17 + 43.5t + -43.5t + 4.5t2 + -4.5t2

Combine like terms: 17 + -17 = 0
64999983 + -43.5t + -4.5t2 = 0 + 43.5t + -43.5t + 4.5t2 + -4.5t2
64999983 + -43.5t + -4.5t2 = 43.5t + -43.5t + 4.5t2 + -4.5t2

Combine like terms: 43.5t + -43.5t = 0.0
64999983 + -43.5t + -4.5t2 = 0.0 + 4.5t2 + -4.5t2
64999983 + -43.5t + -4.5t2 = 4.5t2 + -4.5t2

Combine like terms: 4.5t2 + -4.5t2 = 0.0
64999983 + -43.5t + -4.5t2 = 0.0

Begin completing the square.  Divide all terms by
-4.5 the coefficient of the squared term: 

Divide each side by '-4.5'.
-14444440.67 + 9.666666667t + t2 = 0

Move the constant term to the right:

Add '14444440.67' to each side of the equation.
-14444440.67 + 9.666666667t + 14444440.67 + t2 = 0 + 14444440.67

Reorder the terms:
-14444440.67 + 14444440.67 + 9.666666667t + t2 = 0 + 14444440.67

Combine like terms: -14444440.67 + 14444440.67 = 0.00
0.00 + 9.666666667t + t2 = 0 + 14444440.67
9.666666667t + t2 = 0 + 14444440.67

Combine like terms: 0 + 14444440.67 = 14444440.67
9.666666667t + t2 = 14444440.67

The t term is 9.666666667t.  Take half its coefficient (4.833333334).
Square it (23.36111112) and add it to both sides.

Add '23.36111112' to each side of the equation.
9.666666667t + 23.36111112 + t2 = 14444440.67 + 23.36111112

Reorder the terms:
23.36111112 + 9.666666667t + t2 = 14444440.67 + 23.36111112

Combine like terms: 14444440.67 + 23.36111112 = 14444464.03111112
23.36111112 + 9.666666667t + t2 = 14444464.03111112

Factor a perfect square on the left side:
(t + 4.833333334)(t + 4.833333334) = 14444464.03111112

Calculate the square root of the right side: 3800.587327126

Break this problem into two subproblems by setting 
(t + 4.833333334) equal to 3800.587327126 and -3800.587327126.


Subproblem 1
t + 4.833333334 = 3800.587327126

Simplifying
t + 4.833333334 = 3800.587327126

Reorder the terms:
4.833333334 + t = 3800.587327126

Solving
4.833333334 + t = 3800.587327126

Solving for variable 't'.

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

Add '-4.833333334' to each side of the equation.
4.833333334 + -4.833333334 + t = 3800.587327126 + -4.833333334

Combine like terms: 4.833333334 + -4.833333334 = 0.000000000
0.000000000 + t = 3800.587327126 + -4.833333334
t = 3800.587327126 + -4.833333334

Combine like terms: 3800.587327126 + -4.833333334 = 3795.753993792
t = 3795.753993792

Simplifying
t = 3795.753993792


Subproblem 2
t + 4.833333334 = -3800.587327126

Simplifying
t + 4.833333334 = -3800.587327126

Reorder the terms:
4.833333334 + t = -3800.587327126

Solving
4.833333334 + t = -3800.587327126

Solving for variable 't'.

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

Add '-4.833333334' to each side of the equation.
4.833333334 + -4.833333334 + t = -3800.587327126 + -4.833333334

Combine like terms: 4.833333334 + -4.833333334 = 0.000000000
0.000000000 + t = -3800.587327126 + -4.833333334
t = -3800.587327126 + -4.833333334

Combine like terms: -3800.587327126 + -4.833333334 = -3805.42066046
t = -3805.42066046

Simplifying
t = -3805.42066046


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3795.753993792, -3805.42066046}

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