-5t^2-240t+1734=0

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Solution for -5t^2-240t+1734=0 equation: 


Simplifying
-5t2 + -240t + 1734 = 0

Reorder the terms:
1734 + -240t + -5t2 = 0

Solving
1734 + -240t + -5t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-346.8 + 48t + t2 = 0

Move the constant term to the right:

Add '346.8' to each side of the equation.
-346.8 + 48t + 346.8 + t2 = 0 + 346.8

Reorder the terms:
-346.8 + 346.8 + 48t + t2 = 0 + 346.8

Combine like terms: -346.8 + 346.8 = 0.0
0.0 + 48t + t2 = 0 + 346.8
48t + t2 = 0 + 346.8

Combine like terms: 0 + 346.8 = 346.8
48t + t2 = 346.8

The t term is 48t.  Take half its coefficient (24).
Square it (576) and add it to both sides.

Add '576' to each side of the equation.
48t + 576 + t2 = 346.8 + 576

Reorder the terms:
576 + 48t + t2 = 346.8 + 576

Combine like terms: 346.8 + 576 = 922.8
576 + 48t + t2 = 922.8

Factor a perfect square on the left side:
(t + 24)(t + 24) = 922.8

Calculate the square root of the right side: 30.377623344

Break this problem into two subproblems by setting 
(t + 24) equal to 30.377623344 and -30.377623344.


Subproblem 1
t + 24 = 30.377623344

Simplifying
t + 24 = 30.377623344

Reorder the terms:
24 + t = 30.377623344

Solving
24 + t = 30.377623344

Solving for variable 't'.

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

Add '-24' to each side of the equation.
24 + -24 + t = 30.377623344 + -24

Combine like terms: 24 + -24 = 0
0 + t = 30.377623344 + -24
t = 30.377623344 + -24

Combine like terms: 30.377623344 + -24 = 6.377623344
t = 6.377623344

Simplifying
t = 6.377623344


Subproblem 2
t + 24 = -30.377623344

Simplifying
t + 24 = -30.377623344

Reorder the terms:
24 + t = -30.377623344

Solving
24 + t = -30.377623344

Solving for variable 't'.

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

Add '-24' to each side of the equation.
24 + -24 + t = -30.377623344 + -24

Combine like terms: 24 + -24 = 0
0 + t = -30.377623344 + -24
t = -30.377623344 + -24

Combine like terms: -30.377623344 + -24 = -54.377623344
t = -54.377623344

Simplifying
t = -54.377623344


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.377623344, -54.377623344}

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