-.072t^2+1.278t-3.404=0

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Solution for -.072t^2+1.278t-3.404=0 equation: 


Simplifying
-0.072t2 + 1.278t + -3.404 = 0

Reorder the terms:
-3.404 + 1.278t + -0.072t2 = 0

Solving
-3.404 + 1.278t + -0.072t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-0.072 the coefficient of the squared term: 

Divide each side by '-0.072'.
47.27777778 + -17.75t + t2 = 0

Move the constant term to the right:

Add '-47.27777778' to each side of the equation.
47.27777778 + -17.75t + -47.27777778 + t2 = 0 + -47.27777778

Reorder the terms:
47.27777778 + -47.27777778 + -17.75t + t2 = 0 + -47.27777778

Combine like terms: 47.27777778 + -47.27777778 = 0.00000000
0.00000000 + -17.75t + t2 = 0 + -47.27777778
-17.75t + t2 = 0 + -47.27777778

Combine like terms: 0 + -47.27777778 = -47.27777778
-17.75t + t2 = -47.27777778

The t term is -17.75t.  Take half its coefficient (-8.875).
Square it (78.765625) and add it to both sides.

Add '78.765625' to each side of the equation.
-17.75t + 78.765625 + t2 = -47.27777778 + 78.765625

Reorder the terms:
78.765625 + -17.75t + t2 = -47.27777778 + 78.765625

Combine like terms: -47.27777778 + 78.765625 = 31.48784722
78.765625 + -17.75t + t2 = 31.48784722

Factor a perfect square on the left side:
(t + -8.875)(t + -8.875) = 31.48784722

Calculate the square root of the right side: 5.61140332

Break this problem into two subproblems by setting 
(t + -8.875) equal to 5.61140332 and -5.61140332.


Subproblem 1
t + -8.875 = 5.61140332

Simplifying
t + -8.875 = 5.61140332

Reorder the terms:
-8.875 + t = 5.61140332

Solving
-8.875 + t = 5.61140332

Solving for variable 't'.

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

Add '8.875' to each side of the equation.
-8.875 + 8.875 + t = 5.61140332 + 8.875

Combine like terms: -8.875 + 8.875 = 0.000
0.000 + t = 5.61140332 + 8.875
t = 5.61140332 + 8.875

Combine like terms: 5.61140332 + 8.875 = 14.48640332
t = 14.48640332

Simplifying
t = 14.48640332


Subproblem 2
t + -8.875 = -5.61140332

Simplifying
t + -8.875 = -5.61140332

Reorder the terms:
-8.875 + t = -5.61140332

Solving
-8.875 + t = -5.61140332

Solving for variable 't'.

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

Add '8.875' to each side of the equation.
-8.875 + 8.875 + t = -5.61140332 + 8.875

Combine like terms: -8.875 + 8.875 = 0.000
0.000 + t = -5.61140332 + 8.875
t = -5.61140332 + 8.875

Combine like terms: -5.61140332 + 8.875 = 3.26359668
t = 3.26359668

Simplifying
t = 3.26359668


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {14.48640332, 3.26359668}

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