2=2t^2-10t

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Solution for 2=2t^2-10t equation: 


Simplifying
2 = 2t2 + -10t

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

Solving
2 = -10t + 2t2

Solving for variable 't'.

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

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 5t + -1t2) = 0

Ignore the factor 2.

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

Simplifying
1 + 5t + -1t2 = 0

Solving
1 + 5t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1 + -5t + t2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -5t + 1 + t2 = 0 + 1

Reorder the terms:
-1 + 1 + -5t + t2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5t + t2 = 0 + 1
-5t + t2 = 0 + 1

Combine like terms: 0 + 1 = 1
-5t + t2 = 1

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 = 1 + 6.25

Reorder the terms:
6.25 + -5t + t2 = 1 + 6.25

Combine like terms: 1 + 6.25 = 7.25
6.25 + -5t + t2 = 7.25

Factor a perfect square on the left side:
(t + -2.5)(t + -2.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(t + -2.5) equal to 2.692582404 and -2.692582404.


Subproblem 1
t + -2.5 = 2.692582404

Simplifying
t + -2.5 = 2.692582404

Reorder the terms:
-2.5 + t = 2.692582404

Solving
-2.5 + t = 2.692582404

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 = 2.692582404 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = 2.692582404 + 2.5
t = 2.692582404 + 2.5

Combine like terms: 2.692582404 + 2.5 = 5.192582404
t = 5.192582404

Simplifying
t = 5.192582404


Subproblem 2
t + -2.5 = -2.692582404

Simplifying
t + -2.5 = -2.692582404

Reorder the terms:
-2.5 + t = -2.692582404

Solving
-2.5 + t = -2.692582404

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 = -2.692582404 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = -2.692582404 + 2.5
t = -2.692582404 + 2.5

Combine like terms: -2.692582404 + 2.5 = -0.192582404
t = -0.192582404

Simplifying
t = -0.192582404


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.192582404, -0.192582404}
Solution
t = {5.192582404, -0.192582404}

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