0=t^2-8t+8

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Solution for 0=t^2-8t+8 equation: 


Simplifying
0 = t2 + -8t + 8

Reorder the terms:
0 = 8 + -8t + t2

Solving
0 = 8 + -8t + t2

Solving for variable 't'.

Combine like terms: 0 + -8 = -8
-8 + 8t + -1t2 = 8 + -8t + t2 + -8 + 8t + -1t2

Reorder the terms:
-8 + 8t + -1t2 = 8 + -8 + -8t + 8t + t2 + -1t2

Combine like terms: 8 + -8 = 0
-8 + 8t + -1t2 = 0 + -8t + 8t + t2 + -1t2
-8 + 8t + -1t2 = -8t + 8t + t2 + -1t2

Combine like terms: -8t + 8t = 0
-8 + 8t + -1t2 = 0 + t2 + -1t2
-8 + 8t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-8 + 8t + -1t2 = 0

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

Divide each side by '-1'.
8 + -8t + t2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -8t + -8 + t2 = 0 + -8

Reorder the terms:
8 + -8 + -8t + t2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -8t + t2 = 0 + -8
-8t + t2 = 0 + -8

Combine like terms: 0 + -8 = -8
-8t + t2 = -8

The t term is -8t.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8t + 16 + t2 = -8 + 16

Reorder the terms:
16 + -8t + t2 = -8 + 16

Combine like terms: -8 + 16 = 8
16 + -8t + t2 = 8

Factor a perfect square on the left side:
(t + -4)(t + -4) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(t + -4) equal to 2.828427125 and -2.828427125.


Subproblem 1
t + -4 = 2.828427125

Simplifying
t + -4 = 2.828427125

Reorder the terms:
-4 + t = 2.828427125

Solving
-4 + t = 2.828427125

Solving for variable 't'.

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

Add '4' to each side of the equation.
-4 + 4 + t = 2.828427125 + 4

Combine like terms: -4 + 4 = 0
0 + t = 2.828427125 + 4
t = 2.828427125 + 4

Combine like terms: 2.828427125 + 4 = 6.828427125
t = 6.828427125

Simplifying
t = 6.828427125


Subproblem 2
t + -4 = -2.828427125

Simplifying
t + -4 = -2.828427125

Reorder the terms:
-4 + t = -2.828427125

Solving
-4 + t = -2.828427125

Solving for variable 't'.

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

Add '4' to each side of the equation.
-4 + 4 + t = -2.828427125 + 4

Combine like terms: -4 + 4 = 0
0 + t = -2.828427125 + 4
t = -2.828427125 + 4

Combine like terms: -2.828427125 + 4 = 1.171572875
t = 1.171572875

Simplifying
t = 1.171572875


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.828427125, 1.171572875}

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