9t^2-38t+19=0

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Solution for 9t^2-38t+19=0 equation: 


Simplifying
9t2 + -38t + 19 = 0

Reorder the terms:
19 + -38t + 9t2 = 0

Solving
19 + -38t + 9t2 = 0

Solving for variable 't'.

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

Divide each side by '9'.
2.111111111 + -4.222222222t + t2 = 0

Move the constant term to the right:

Add '-2.111111111' to each side of the equation.
2.111111111 + -4.222222222t + -2.111111111 + t2 = 0 + -2.111111111

Reorder the terms:
2.111111111 + -2.111111111 + -4.222222222t + t2 = 0 + -2.111111111

Combine like terms: 2.111111111 + -2.111111111 = 0.000000000
0.000000000 + -4.222222222t + t2 = 0 + -2.111111111
-4.222222222t + t2 = 0 + -2.111111111

Combine like terms: 0 + -2.111111111 = -2.111111111
-4.222222222t + t2 = -2.111111111

The t term is -4.222222222t.  Take half its coefficient (-2.111111111).
Square it (4.456790123) and add it to both sides.

Add '4.456790123' to each side of the equation.
-4.222222222t + 4.456790123 + t2 = -2.111111111 + 4.456790123

Reorder the terms:
4.456790123 + -4.222222222t + t2 = -2.111111111 + 4.456790123

Combine like terms: -2.111111111 + 4.456790123 = 2.345679012
4.456790123 + -4.222222222t + t2 = 2.345679012

Factor a perfect square on the left side:
(t + -2.111111111)(t + -2.111111111) = 2.345679012

Calculate the square root of the right side: 1.531560972

Break this problem into two subproblems by setting 
(t + -2.111111111) equal to 1.531560972 and -1.531560972.


Subproblem 1
t + -2.111111111 = 1.531560972

Simplifying
t + -2.111111111 = 1.531560972

Reorder the terms:
-2.111111111 + t = 1.531560972

Solving
-2.111111111 + t = 1.531560972

Solving for variable 't'.

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

Add '2.111111111' to each side of the equation.
-2.111111111 + 2.111111111 + t = 1.531560972 + 2.111111111

Combine like terms: -2.111111111 + 2.111111111 = 0.000000000
0.000000000 + t = 1.531560972 + 2.111111111
t = 1.531560972 + 2.111111111

Combine like terms: 1.531560972 + 2.111111111 = 3.642672083
t = 3.642672083

Simplifying
t = 3.642672083


Subproblem 2
t + -2.111111111 = -1.531560972

Simplifying
t + -2.111111111 = -1.531560972

Reorder the terms:
-2.111111111 + t = -1.531560972

Solving
-2.111111111 + t = -1.531560972

Solving for variable 't'.

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

Add '2.111111111' to each side of the equation.
-2.111111111 + 2.111111111 + t = -1.531560972 + 2.111111111

Combine like terms: -2.111111111 + 2.111111111 = 0.000000000
0.000000000 + t = -1.531560972 + 2.111111111
t = -1.531560972 + 2.111111111

Combine like terms: -1.531560972 + 2.111111111 = 0.579550139
t = 0.579550139

Simplifying
t = 0.579550139


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.642672083, 0.579550139}

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