3t^2-22t-24=0

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Solution for 3t^2-22t-24=0 equation: 


Simplifying
3t2 + -22t + -24 = 0

Reorder the terms:
-24 + -22t + 3t2 = 0

Solving
-24 + -22t + 3t2 = 0

Solving for variable 't'.

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

Divide each side by '3'.
-8 + -7.333333333t + t2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -7.333333333t + 8 + t2 = 0 + 8

Reorder the terms:
-8 + 8 + -7.333333333t + t2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -7.333333333t + t2 = 0 + 8
-7.333333333t + t2 = 0 + 8

Combine like terms: 0 + 8 = 8
-7.333333333t + t2 = 8

The t term is -7.333333333t.  Take half its coefficient (-3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
-7.333333333t + 13.44444445 + t2 = 8 + 13.44444445

Reorder the terms:
13.44444445 + -7.333333333t + t2 = 8 + 13.44444445

Combine like terms: 8 + 13.44444445 = 21.44444445
13.44444445 + -7.333333333t + t2 = 21.44444445

Factor a perfect square on the left side:
(t + -3.666666667)(t + -3.666666667) = 21.44444445

Calculate the square root of the right side: 4.630814664

Break this problem into two subproblems by setting 
(t + -3.666666667) equal to 4.630814664 and -4.630814664.


Subproblem 1
t + -3.666666667 = 4.630814664

Simplifying
t + -3.666666667 = 4.630814664

Reorder the terms:
-3.666666667 + t = 4.630814664

Solving
-3.666666667 + t = 4.630814664

Solving for variable 't'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + t = 4.630814664 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + t = 4.630814664 + 3.666666667
t = 4.630814664 + 3.666666667

Combine like terms: 4.630814664 + 3.666666667 = 8.297481331
t = 8.297481331

Simplifying
t = 8.297481331


Subproblem 2
t + -3.666666667 = -4.630814664

Simplifying
t + -3.666666667 = -4.630814664

Reorder the terms:
-3.666666667 + t = -4.630814664

Solving
-3.666666667 + t = -4.630814664

Solving for variable 't'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + t = -4.630814664 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + t = -4.630814664 + 3.666666667
t = -4.630814664 + 3.666666667

Combine like terms: -4.630814664 + 3.666666667 = -0.964147997
t = -0.964147997

Simplifying
t = -0.964147997


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {8.297481331, -0.964147997}

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