(2(t^2))-8t=-4

Solution for (2(t^2))-8t=-4 equation:

Simplifying
(2(t2)) + -8t = -4

Reorder the terms:
-8t + (2t2) = -4

Solving
-8t + (2t2) = -4

Solving for variable 't'.

Reorder the terms:
4 + -8t + (2t2) = -4 + 4

Combine like terms: -4 + 4 = 0
4 + -8t + (2t2) = 0

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

Ignore the factor 2.
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}