3t^2-39t-21=0

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Solution for 3t^2-39t-21=0 equation: 


Simplifying
3t2 + -39t + -21 = 0

Reorder the terms:
-21 + -39t + 3t2 = 0

Solving
-21 + -39t + 3t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + -13t + t2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-7 + -13t + t2)' equal to zero and attempt to solve:

Simplifying
-7 + -13t + t2 = 0

Solving
-7 + -13t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -13t + 7 + t2 = 0 + 7

Reorder the terms:
-7 + 7 + -13t + t2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -13t + t2 = 0 + 7
-13t + t2 = 0 + 7

Combine like terms: 0 + 7 = 7
-13t + t2 = 7

The t term is -13t.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13t + 42.25 + t2 = 7 + 42.25

Reorder the terms:
42.25 + -13t + t2 = 7 + 42.25

Combine like terms: 7 + 42.25 = 49.25
42.25 + -13t + t2 = 49.25

Factor a perfect square on the left side:
(t + -6.5)(t + -6.5) = 49.25

Calculate the square root of the right side: 7.017834424

Break this problem into two subproblems by setting 
(t + -6.5) equal to 7.017834424 and -7.017834424.


Subproblem 1
t + -6.5 = 7.017834424

Simplifying
t + -6.5 = 7.017834424

Reorder the terms:
-6.5 + t = 7.017834424

Solving
-6.5 + t = 7.017834424

Solving for variable 't'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + t = 7.017834424 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + t = 7.017834424 + 6.5
t = 7.017834424 + 6.5

Combine like terms: 7.017834424 + 6.5 = 13.517834424
t = 13.517834424

Simplifying
t = 13.517834424


Subproblem 2
t + -6.5 = -7.017834424

Simplifying
t + -6.5 = -7.017834424

Reorder the terms:
-6.5 + t = -7.017834424

Solving
-6.5 + t = -7.017834424

Solving for variable 't'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + t = -7.017834424 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + t = -7.017834424 + 6.5
t = -7.017834424 + 6.5

Combine like terms: -7.017834424 + 6.5 = -0.517834424
t = -0.517834424

Simplifying
t = -0.517834424


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {13.517834424, -0.517834424}
Solution
t = {13.517834424, -0.517834424}

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