t^2-18t+19=0

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Solution for t^2-18t+19=0 equation:


Simplifying
t2 + -18t + 19 = 0

Reorder the terms:
19 + -18t + t2 = 0

Solving
19 + -18t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-19' to each side of the equation.
19 + -18t + -19 + t2 = 0 + -19

Reorder the terms:
19 + -19 + -18t + t2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -18t + t2 = 0 + -19
-18t + t2 = 0 + -19

Combine like terms: 0 + -19 = -19
-18t + t2 = -19

The t term is -18t.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18t + 81 + t2 = -19 + 81

Reorder the terms:
81 + -18t + t2 = -19 + 81

Combine like terms: -19 + 81 = 62
81 + -18t + t2 = 62

Factor a perfect square on the left side:
(t + -9)(t + -9) = 62

Calculate the square root of the right side: 7.874007874

Break this problem into two subproblems by setting 
(t + -9) equal to 7.874007874 and -7.874007874.


Subproblem 1
t + -9 = 7.874007874

Simplifying
t + -9 = 7.874007874

Reorder the terms:
-9 + t = 7.874007874

Solving
-9 + t = 7.874007874

Solving for variable 't'.

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

Add '9' to each side of the equation.
-9 + 9 + t = 7.874007874 + 9

Combine like terms: -9 + 9 = 0
0 + t = 7.874007874 + 9
t = 7.874007874 + 9

Combine like terms: 7.874007874 + 9 = 16.874007874
t = 16.874007874

Simplifying
t = 16.874007874


Subproblem 2
t + -9 = -7.874007874

Simplifying
t + -9 = -7.874007874

Reorder the terms:
-9 + t = -7.874007874

Solving
-9 + t = -7.874007874

Solving for variable 't'.

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

Add '9' to each side of the equation.
-9 + 9 + t = -7.874007874 + 9

Combine like terms: -9 + 9 = 0
0 + t = -7.874007874 + 9
t = -7.874007874 + 9

Combine like terms: -7.874007874 + 9 = 1.125992126
t = 1.125992126

Simplifying
t = 1.125992126


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {16.874007874, 1.125992126}

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