12=2+25t-5t^2

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Solution for 12=2+25t-5t^2 equation: 


Simplifying
12 = 2 + 25t + -5t2

Solving
12 = 2 + 25t + -5t2

Solving for variable 't'.

Combine like terms: 12 + -2 = 10
10 + -25t + 5t2 = 2 + 25t + -5t2 + -2 + -25t + 5t2

Reorder the terms:
10 + -25t + 5t2 = 2 + -2 + 25t + -25t + -5t2 + 5t2

Combine like terms: 2 + -2 = 0
10 + -25t + 5t2 = 0 + 25t + -25t + -5t2 + 5t2
10 + -25t + 5t2 = 25t + -25t + -5t2 + 5t2

Combine like terms: 25t + -25t = 0
10 + -25t + 5t2 = 0 + -5t2 + 5t2
10 + -25t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
10 + -25t + 5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + -5t + t2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(2 + -5t + t2)' equal to zero and attempt to solve:

Simplifying
2 + -5t + t2 = 0

Solving
2 + -5t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -5t + -2 + t2 = 0 + -2

Reorder the terms:
2 + -2 + -5t + t2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5t + t2 = 0 + -2
-5t + t2 = 0 + -2

Combine like terms: 0 + -2 = -2
-5t + t2 = -2

The t term is -5t.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5t + 6.25 + t2 = -2 + 6.25

Reorder the terms:
6.25 + -5t + t2 = -2 + 6.25

Combine like terms: -2 + 6.25 = 4.25
6.25 + -5t + t2 = 4.25

Factor a perfect square on the left side:
(t + -2.5)(t + -2.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(t + -2.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
t + -2.5 = 2.061552813

Simplifying
t + -2.5 = 2.061552813

Reorder the terms:
-2.5 + t = 2.061552813

Solving
-2.5 + t = 2.061552813

Solving for variable 't'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + t = 2.061552813 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = 2.061552813 + 2.5
t = 2.061552813 + 2.5

Combine like terms: 2.061552813 + 2.5 = 4.561552813
t = 4.561552813

Simplifying
t = 4.561552813


Subproblem 2
t + -2.5 = -2.061552813

Simplifying
t + -2.5 = -2.061552813

Reorder the terms:
-2.5 + t = -2.061552813

Solving
-2.5 + t = -2.061552813

Solving for variable 't'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + t = -2.061552813 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = -2.061552813 + 2.5
t = -2.061552813 + 2.5

Combine like terms: -2.061552813 + 2.5 = 0.438447187
t = 0.438447187

Simplifying
t = 0.438447187


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.561552813, 0.438447187}
Solution
t = {4.561552813, 0.438447187}

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