=t^2-4t+0.8

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Solution for =t^2-4t+0.8 equation: 


Simplifying
0 = t2 + -4t + 0.8

Reorder the terms:
0 = 0.8 + -4t + t2

Solving
0 = 0.8 + -4t + t2

Solving for variable 't'.

Combine like terms: 0 + -0.8 = -0.8
-0.8 + 4t + -1t2 = 0.8 + -4t + t2 + -0.8 + 4t + -1t2

Reorder the terms:
-0.8 + 4t + -1t2 = 0.8 + -0.8 + -4t + 4t + t2 + -1t2

Combine like terms: 0.8 + -0.8 = 0.0
-0.8 + 4t + -1t2 = 0.0 + -4t + 4t + t2 + -1t2
-0.8 + 4t + -1t2 = -4t + 4t + t2 + -1t2

Combine like terms: -4t + 4t = 0
-0.8 + 4t + -1t2 = 0 + t2 + -1t2
-0.8 + 4t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-0.8 + 4t + -1t2 = 0

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

Divide each side by '-1'.
0.8 + -4t + t2 = 0

Move the constant term to the right:

Add '-0.8' to each side of the equation.
0.8 + -4t + -0.8 + t2 = 0 + -0.8

Reorder the terms:
0.8 + -0.8 + -4t + t2 = 0 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + -4t + t2 = 0 + -0.8
-4t + t2 = 0 + -0.8

Combine like terms: 0 + -0.8 = -0.8
-4t + t2 = -0.8

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 = -0.8 + 4

Reorder the terms:
4 + -4t + t2 = -0.8 + 4

Combine like terms: -0.8 + 4 = 3.2
4 + -4t + t2 = 3.2

Factor a perfect square on the left side:
(t + -2)(t + -2) = 3.2

Calculate the square root of the right side: 1.788854382

Break this problem into two subproblems by setting 
(t + -2) equal to 1.788854382 and -1.788854382.


Subproblem 1
t + -2 = 1.788854382

Simplifying
t + -2 = 1.788854382

Reorder the terms:
-2 + t = 1.788854382

Solving
-2 + t = 1.788854382

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 = 1.788854382 + 2

Combine like terms: -2 + 2 = 0
0 + t = 1.788854382 + 2
t = 1.788854382 + 2

Combine like terms: 1.788854382 + 2 = 3.788854382
t = 3.788854382

Simplifying
t = 3.788854382


Subproblem 2
t + -2 = -1.788854382

Simplifying
t + -2 = -1.788854382

Reorder the terms:
-2 + t = -1.788854382

Solving
-2 + t = -1.788854382

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 = -1.788854382 + 2

Combine like terms: -2 + 2 = 0
0 + t = -1.788854382 + 2
t = -1.788854382 + 2

Combine like terms: -1.788854382 + 2 = 0.211145618
t = 0.211145618

Simplifying
t = 0.211145618


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.788854382, 0.211145618}

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