5t^2-20t+10=0

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Solution for 5t^2-20t+10=0 equation: 


Simplifying
5t2 + -20t + 10 = 0

Reorder the terms:
10 + -20t + 5t2 = 0

Solving
10 + -20t + 5t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + -4t + t2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(2 + -4t + t2)' equal to zero and attempt to solve:

Simplifying
2 + -4t + t2 = 0

Solving
2 + -4t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -4t + -2 + t2 = 0 + -2

Reorder the terms:
2 + -2 + -4t + t2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -4t + t2 = 0 + -2
-4t + t2 = 0 + -2

Combine like terms: 0 + -2 = -2
-4t + t2 = -2

The t term is -4t.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4t + 4 + t2 = -2 + 4

Reorder the terms:
4 + -4t + t2 = -2 + 4

Combine like terms: -2 + 4 = 2
4 + -4t + t2 = 2

Factor a perfect square on the left side:
(t + -2)(t + -2) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(t + -2) equal to 1.414213562 and -1.414213562.


Subproblem 1
t + -2 = 1.414213562

Simplifying
t + -2 = 1.414213562

Reorder the terms:
-2 + t = 1.414213562

Solving
-2 + t = 1.414213562

Solving for variable 't'.

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

Add '2' to each side of the equation.
-2 + 2 + t = 1.414213562 + 2

Combine like terms: -2 + 2 = 0
0 + t = 1.414213562 + 2
t = 1.414213562 + 2

Combine like terms: 1.414213562 + 2 = 3.414213562
t = 3.414213562

Simplifying
t = 3.414213562


Subproblem 2
t + -2 = -1.414213562

Simplifying
t + -2 = -1.414213562

Reorder the terms:
-2 + t = -1.414213562

Solving
-2 + t = -1.414213562

Solving for variable 't'.

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

Add '2' to each side of the equation.
-2 + 2 + t = -1.414213562 + 2

Combine like terms: -2 + 2 = 0
0 + t = -1.414213562 + 2
t = -1.414213562 + 2

Combine like terms: -1.414213562 + 2 = 0.585786438
t = 0.585786438

Simplifying
t = 0.585786438


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.414213562, 0.585786438}
Solution
t = {3.414213562, 0.585786438}

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