0.3t^2-5t+0.3=0

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Solution for 0.3t^2-5t+0.3=0 equation: 


Simplifying
0.3t2 + -5t + 0.3 = 0

Reorder the terms:
0.3 + -5t + 0.3t2 = 0

Solving
0.3 + -5t + 0.3t2 = 0

Solving for variable 't'.

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

Divide each side by '0.3'.
1 + -16.66666667t + t2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -16.66666667t + -1 + t2 = 0 + -1

Reorder the terms:
1 + -1 + -16.66666667t + t2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -16.66666667t + t2 = 0 + -1
-16.66666667t + t2 = 0 + -1

Combine like terms: 0 + -1 = -1
-16.66666667t + t2 = -1

The t term is -16.66666667t.  Take half its coefficient (-8.333333335).
Square it (69.44444447) and add it to both sides.

Add '69.44444447' to each side of the equation.
-16.66666667t + 69.44444447 + t2 = -1 + 69.44444447

Reorder the terms:
69.44444447 + -16.66666667t + t2 = -1 + 69.44444447

Combine like terms: -1 + 69.44444447 = 68.44444447
69.44444447 + -16.66666667t + t2 = 68.44444447

Factor a perfect square on the left side:
(t + -8.333333335)(t + -8.333333335) = 68.44444447

Calculate the square root of the right side: 8.273115766

Break this problem into two subproblems by setting 
(t + -8.333333335) equal to 8.273115766 and -8.273115766.


Subproblem 1
t + -8.333333335 = 8.273115766

Simplifying
t + -8.333333335 = 8.273115766

Reorder the terms:
-8.333333335 + t = 8.273115766

Solving
-8.333333335 + t = 8.273115766

Solving for variable 't'.

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

Add '8.333333335' to each side of the equation.
-8.333333335 + 8.333333335 + t = 8.273115766 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + t = 8.273115766 + 8.333333335
t = 8.273115766 + 8.333333335

Combine like terms: 8.273115766 + 8.333333335 = 16.606449101
t = 16.606449101

Simplifying
t = 16.606449101


Subproblem 2
t + -8.333333335 = -8.273115766

Simplifying
t + -8.333333335 = -8.273115766

Reorder the terms:
-8.333333335 + t = -8.273115766

Solving
-8.333333335 + t = -8.273115766

Solving for variable 't'.

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

Add '8.333333335' to each side of the equation.
-8.333333335 + 8.333333335 + t = -8.273115766 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + t = -8.273115766 + 8.333333335
t = -8.273115766 + 8.333333335

Combine like terms: -8.273115766 + 8.333333335 = 0.060217569
t = 0.060217569

Simplifying
t = 0.060217569


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {16.606449101, 0.060217569}

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