t^2-9t-3.75=0

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Solution for t^2-9t-3.75=0 equation: 


Simplifying
t2 + -9t + -3.75 = 0

Reorder the terms:
-3.75 + -9t + t2 = 0

Solving
-3.75 + -9t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + -9t + 3.75 + t2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + -9t + t2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + -9t + t2 = 0 + 3.75
-9t + t2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
-9t + t2 = 3.75

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 = 3.75 + 20.25

Reorder the terms:
20.25 + -9t + t2 = 3.75 + 20.25

Combine like terms: 3.75 + 20.25 = 24
20.25 + -9t + t2 = 24

Factor a perfect square on the left side:
(t + -4.5)(t + -4.5) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(t + -4.5) equal to 4.898979486 and -4.898979486.


Subproblem 1
t + -4.5 = 4.898979486

Simplifying
t + -4.5 = 4.898979486

Reorder the terms:
-4.5 + t = 4.898979486

Solving
-4.5 + t = 4.898979486

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 = 4.898979486 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + t = 4.898979486 + 4.5
t = 4.898979486 + 4.5

Combine like terms: 4.898979486 + 4.5 = 9.398979486
t = 9.398979486

Simplifying
t = 9.398979486


Subproblem 2
t + -4.5 = -4.898979486

Simplifying
t + -4.5 = -4.898979486

Reorder the terms:
-4.5 + t = -4.898979486

Solving
-4.5 + t = -4.898979486

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 = -4.898979486 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + t = -4.898979486 + 4.5
t = -4.898979486 + 4.5

Combine like terms: -4.898979486 + 4.5 = -0.398979486
t = -0.398979486

Simplifying
t = -0.398979486


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {9.398979486, -0.398979486}

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