6t^2-420t+3549=0

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Solution for 6t^2-420t+3549=0 equation: 


Simplifying
6t2 + -420t + 3549 = 0

Reorder the terms:
3549 + -420t + 6t2 = 0

Solving
3549 + -420t + 6t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1183 + -140t + 2t2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(1183 + -140t + 2t2)' equal to zero and attempt to solve:

Simplifying
1183 + -140t + 2t2 = 0

Solving
1183 + -140t + 2t2 = 0

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

Divide each side by '2'.
591.5 + -70t + t2 = 0

Move the constant term to the right:

Add '-591.5' to each side of the equation.
591.5 + -70t + -591.5 + t2 = 0 + -591.5

Reorder the terms:
591.5 + -591.5 + -70t + t2 = 0 + -591.5

Combine like terms: 591.5 + -591.5 = 0.0
0.0 + -70t + t2 = 0 + -591.5
-70t + t2 = 0 + -591.5

Combine like terms: 0 + -591.5 = -591.5
-70t + t2 = -591.5

The t term is -70t.  Take half its coefficient (-35).
Square it (1225) and add it to both sides.

Add '1225' to each side of the equation.
-70t + 1225 + t2 = -591.5 + 1225

Reorder the terms:
1225 + -70t + t2 = -591.5 + 1225

Combine like terms: -591.5 + 1225 = 633.5
1225 + -70t + t2 = 633.5

Factor a perfect square on the left side:
(t + -35)(t + -35) = 633.5

Calculate the square root of the right side: 25.169425897

Break this problem into two subproblems by setting 
(t + -35) equal to 25.169425897 and -25.169425897.


Subproblem 1
t + -35 = 25.169425897

Simplifying
t + -35 = 25.169425897

Reorder the terms:
-35 + t = 25.169425897

Solving
-35 + t = 25.169425897

Solving for variable 't'.

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

Add '35' to each side of the equation.
-35 + 35 + t = 25.169425897 + 35

Combine like terms: -35 + 35 = 0
0 + t = 25.169425897 + 35
t = 25.169425897 + 35

Combine like terms: 25.169425897 + 35 = 60.169425897
t = 60.169425897

Simplifying
t = 60.169425897


Subproblem 2
t + -35 = -25.169425897

Simplifying
t + -35 = -25.169425897

Reorder the terms:
-35 + t = -25.169425897

Solving
-35 + t = -25.169425897

Solving for variable 't'.

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

Add '35' to each side of the equation.
-35 + 35 + t = -25.169425897 + 35

Combine like terms: -35 + 35 = 0
0 + t = -25.169425897 + 35
t = -25.169425897 + 35

Combine like terms: -25.169425897 + 35 = 9.830574103
t = 9.830574103

Simplifying
t = 9.830574103


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {60.169425897, 9.830574103}
Solution
t = {60.169425897, 9.830574103}

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