6t^2+24t-100=0

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Solution for 6t^2+24t-100=0 equation: 


Simplifying
6t2 + 24t + -100 = 0

Reorder the terms:
-100 + 24t + 6t2 = 0

Solving
-100 + 24t + 6t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + 12t + 3t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-50 + 12t + 3t2)' equal to zero and attempt to solve:

Simplifying
-50 + 12t + 3t2 = 0

Solving
-50 + 12t + 3t2 = 0

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

Divide each side by '3'.
-16.66666667 + 4t + t2 = 0

Move the constant term to the right:

Add '16.66666667' to each side of the equation.
-16.66666667 + 4t + 16.66666667 + t2 = 0 + 16.66666667

Reorder the terms:
-16.66666667 + 16.66666667 + 4t + t2 = 0 + 16.66666667

Combine like terms: -16.66666667 + 16.66666667 = 0.00000000
0.00000000 + 4t + t2 = 0 + 16.66666667
4t + t2 = 0 + 16.66666667

Combine like terms: 0 + 16.66666667 = 16.66666667
4t + t2 = 16.66666667

The t term is 4t.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4t + 4 + t2 = 16.66666667 + 4

Reorder the terms:
4 + 4t + t2 = 16.66666667 + 4

Combine like terms: 16.66666667 + 4 = 20.66666667
4 + 4t + t2 = 20.66666667

Factor a perfect square on the left side:
(t + 2)(t + 2) = 20.66666667

Calculate the square root of the right side: 4.546060566

Break this problem into two subproblems by setting 
(t + 2) equal to 4.546060566 and -4.546060566.


Subproblem 1
t + 2 = 4.546060566

Simplifying
t + 2 = 4.546060566

Reorder the terms:
2 + t = 4.546060566

Solving
2 + t = 4.546060566

Solving for variable 't'.

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

Add '-2' to each side of the equation.
2 + -2 + t = 4.546060566 + -2

Combine like terms: 2 + -2 = 0
0 + t = 4.546060566 + -2
t = 4.546060566 + -2

Combine like terms: 4.546060566 + -2 = 2.546060566
t = 2.546060566

Simplifying
t = 2.546060566


Subproblem 2
t + 2 = -4.546060566

Simplifying
t + 2 = -4.546060566

Reorder the terms:
2 + t = -4.546060566

Solving
2 + t = -4.546060566

Solving for variable 't'.

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

Add '-2' to each side of the equation.
2 + -2 + t = -4.546060566 + -2

Combine like terms: 2 + -2 = 0
0 + t = -4.546060566 + -2
t = -4.546060566 + -2

Combine like terms: -4.546060566 + -2 = -6.546060566
t = -6.546060566

Simplifying
t = -6.546060566


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.546060566, -6.546060566}
Solution
t = {2.546060566, -6.546060566}

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