2.5t^2+12t-32=0

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Solution for 2.5t^2+12t-32=0 equation: 


Simplifying
2.5t2 + 12t + -32 = 0

Reorder the terms:
-32 + 12t + 2.5t2 = 0

Solving
-32 + 12t + 2.5t2 = 0

Solving for variable 't'.

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

Divide each side by '2.5'.
-12.8 + 4.8t + t2 = 0

Move the constant term to the right:

Add '12.8' to each side of the equation.
-12.8 + 4.8t + 12.8 + t2 = 0 + 12.8

Reorder the terms:
-12.8 + 12.8 + 4.8t + t2 = 0 + 12.8

Combine like terms: -12.8 + 12.8 = 0.0
0.0 + 4.8t + t2 = 0 + 12.8
4.8t + t2 = 0 + 12.8

Combine like terms: 0 + 12.8 = 12.8
4.8t + t2 = 12.8

The t term is 4.8t.  Take half its coefficient (2.4).
Square it (5.76) and add it to both sides.

Add '5.76' to each side of the equation.
4.8t + 5.76 + t2 = 12.8 + 5.76

Reorder the terms:
5.76 + 4.8t + t2 = 12.8 + 5.76

Combine like terms: 12.8 + 5.76 = 18.56
5.76 + 4.8t + t2 = 18.56

Factor a perfect square on the left side:
(t + 2.4)(t + 2.4) = 18.56

Calculate the square root of the right side: 4.308131846

Break this problem into two subproblems by setting 
(t + 2.4) equal to 4.308131846 and -4.308131846.


Subproblem 1
t + 2.4 = 4.308131846

Simplifying
t + 2.4 = 4.308131846

Reorder the terms:
2.4 + t = 4.308131846

Solving
2.4 + t = 4.308131846

Solving for variable 't'.

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

Add '-2.4' to each side of the equation.
2.4 + -2.4 + t = 4.308131846 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + t = 4.308131846 + -2.4
t = 4.308131846 + -2.4

Combine like terms: 4.308131846 + -2.4 = 1.908131846
t = 1.908131846

Simplifying
t = 1.908131846


Subproblem 2
t + 2.4 = -4.308131846

Simplifying
t + 2.4 = -4.308131846

Reorder the terms:
2.4 + t = -4.308131846

Solving
2.4 + t = -4.308131846

Solving for variable 't'.

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

Add '-2.4' to each side of the equation.
2.4 + -2.4 + t = -4.308131846 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + t = -4.308131846 + -2.4
t = -4.308131846 + -2.4

Combine like terms: -4.308131846 + -2.4 = -6.708131846
t = -6.708131846

Simplifying
t = -6.708131846


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.908131846, -6.708131846}

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