6t^2-60t+10=0

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Solution for 6t^2-60t+10=0 equation: 


Simplifying
6t2 + -60t + 10 = 0

Reorder the terms:
10 + -60t + 6t2 = 0

Solving
10 + -60t + 6t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -30t + 3t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -30t + 3t2)' equal to zero and attempt to solve:

Simplifying
5 + -30t + 3t2 = 0

Solving
5 + -30t + 3t2 = 0

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

Divide each side by '3'.
1.666666667 + -10t + t2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -10t + -1.666666667 + t2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -10t + t2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -10t + t2 = 0 + -1.666666667
-10t + t2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-10t + t2 = -1.666666667

The t term is -10t.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10t + 25 + t2 = -1.666666667 + 25

Reorder the terms:
25 + -10t + t2 = -1.666666667 + 25

Combine like terms: -1.666666667 + 25 = 23.333333333
25 + -10t + t2 = 23.333333333

Factor a perfect square on the left side:
(t + -5)(t + -5) = 23.333333333

Calculate the square root of the right side: 4.830458915

Break this problem into two subproblems by setting 
(t + -5) equal to 4.830458915 and -4.830458915.


Subproblem 1
t + -5 = 4.830458915

Simplifying
t + -5 = 4.830458915

Reorder the terms:
-5 + t = 4.830458915

Solving
-5 + t = 4.830458915

Solving for variable 't'.

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

Add '5' to each side of the equation.
-5 + 5 + t = 4.830458915 + 5

Combine like terms: -5 + 5 = 0
0 + t = 4.830458915 + 5
t = 4.830458915 + 5

Combine like terms: 4.830458915 + 5 = 9.830458915
t = 9.830458915

Simplifying
t = 9.830458915


Subproblem 2
t + -5 = -4.830458915

Simplifying
t + -5 = -4.830458915

Reorder the terms:
-5 + t = -4.830458915

Solving
-5 + t = -4.830458915

Solving for variable 't'.

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

Add '5' to each side of the equation.
-5 + 5 + t = -4.830458915 + 5

Combine like terms: -5 + 5 = 0
0 + t = -4.830458915 + 5
t = -4.830458915 + 5

Combine like terms: -4.830458915 + 5 = 0.169541085
t = 0.169541085

Simplifying
t = 0.169541085


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {9.830458915, 0.169541085}
Solution
t = {9.830458915, 0.169541085}

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