t^2-t-0.5=0

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Solution for t^2-t-0.5=0 equation: 


Simplifying
t2 + -1t + -0.5 = 0

Reorder the terms:
-0.5 + -1t + t2 = 0

Solving
-0.5 + -1t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -1t + 0.5 + t2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -1t + t2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -1t + t2 = 0 + 0.5
-1t + t2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-1t + t2 = 0.5

The t term is -1t.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1t + 0.25 + t2 = 0.5 + 0.25

Reorder the terms:
0.25 + -1t + t2 = 0.5 + 0.25

Combine like terms: 0.5 + 0.25 = 0.75
0.25 + -1t + t2 = 0.75

Factor a perfect square on the left side:
(t + -0.5)(t + -0.5) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(t + -0.5) equal to 0.866025404 and -0.866025404.


Subproblem 1
t + -0.5 = 0.866025404

Simplifying
t + -0.5 = 0.866025404

Reorder the terms:
-0.5 + t = 0.866025404

Solving
-0.5 + t = 0.866025404

Solving for variable 't'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + t = 0.866025404 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + t = 0.866025404 + 0.5
t = 0.866025404 + 0.5

Combine like terms: 0.866025404 + 0.5 = 1.366025404
t = 1.366025404

Simplifying
t = 1.366025404


Subproblem 2
t + -0.5 = -0.866025404

Simplifying
t + -0.5 = -0.866025404

Reorder the terms:
-0.5 + t = -0.866025404

Solving
-0.5 + t = -0.866025404

Solving for variable 't'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + t = -0.866025404 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + t = -0.866025404 + 0.5
t = -0.866025404 + 0.5

Combine like terms: -0.866025404 + 0.5 = -0.366025404
t = -0.366025404

Simplifying
t = -0.366025404


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.366025404, -0.366025404}

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