9*t=9.8-t^2

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Solution for 9*t=9.8-t^2 equation: 


Simplifying
9t = 9.8 + -1t2

Solving
9t = 9.8 + -1t2

Solving for variable 't'.

Reorder the terms:
-9.8 + 9t + t2 = 9.8 + -1t2 + -9.8 + t2

Reorder the terms:
-9.8 + 9t + t2 = 9.8 + -9.8 + -1t2 + t2

Combine like terms: 9.8 + -9.8 = 0.0
-9.8 + 9t + t2 = 0.0 + -1t2 + t2
-9.8 + 9t + t2 = -1t2 + t2

Combine like terms: -1t2 + t2 = 0
-9.8 + 9t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9.8' to each side of the equation.
-9.8 + 9t + 9.8 + t2 = 0 + 9.8

Reorder the terms:
-9.8 + 9.8 + 9t + t2 = 0 + 9.8

Combine like terms: -9.8 + 9.8 = 0.0
0.0 + 9t + t2 = 0 + 9.8
9t + t2 = 0 + 9.8

Combine like terms: 0 + 9.8 = 9.8
9t + t2 = 9.8

The t term is 9t.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9t + 20.25 + t2 = 9.8 + 20.25

Reorder the terms:
20.25 + 9t + t2 = 9.8 + 20.25

Combine like terms: 9.8 + 20.25 = 30.05
20.25 + 9t + t2 = 30.05

Factor a perfect square on the left side:
(t + 4.5)(t + 4.5) = 30.05

Calculate the square root of the right side: 5.481788029

Break this problem into two subproblems by setting 
(t + 4.5) equal to 5.481788029 and -5.481788029.


Subproblem 1
t + 4.5 = 5.481788029

Simplifying
t + 4.5 = 5.481788029

Reorder the terms:
4.5 + t = 5.481788029

Solving
4.5 + t = 5.481788029

Solving for variable 't'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + t = 5.481788029 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + t = 5.481788029 + -4.5
t = 5.481788029 + -4.5

Combine like terms: 5.481788029 + -4.5 = 0.981788029
t = 0.981788029

Simplifying
t = 0.981788029


Subproblem 2
t + 4.5 = -5.481788029

Simplifying
t + 4.5 = -5.481788029

Reorder the terms:
4.5 + t = -5.481788029

Solving
4.5 + t = -5.481788029

Solving for variable 't'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + t = -5.481788029 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + t = -5.481788029 + -4.5
t = -5.481788029 + -4.5

Combine like terms: -5.481788029 + -4.5 = -9.981788029
t = -9.981788029

Simplifying
t = -9.981788029


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.981788029, -9.981788029}

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