9000(26+16t-t^2)=0

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Solution for 9000(26+16t-t^2)=0 equation: 


Simplifying
9000(26 + 16t + -1t2) = 0
(26 * 9000 + 16t * 9000 + -1t2 * 9000) = 0
(234000 + 144000t + -9000t2) = 0

Solving
234000 + 144000t + -9000t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '9000'.
9000(26 + 16t + -1t2) = 0

Ignore the factor 9000.

Subproblem 1
Set the factor '(26 + 16t + -1t2)' equal to zero and attempt to solve:

Simplifying
26 + 16t + -1t2 = 0

Solving
26 + 16t + -1t2 = 0

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

Divide each side by '-1'.
-26 + -16t + t2 = 0

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + -16t + 26 + t2 = 0 + 26

Reorder the terms:
-26 + 26 + -16t + t2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -16t + t2 = 0 + 26
-16t + t2 = 0 + 26

Combine like terms: 0 + 26 = 26
-16t + t2 = 26

The t term is -16t.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16t + 64 + t2 = 26 + 64

Reorder the terms:
64 + -16t + t2 = 26 + 64

Combine like terms: 26 + 64 = 90
64 + -16t + t2 = 90

Factor a perfect square on the left side:
(t + -8)(t + -8) = 90

Calculate the square root of the right side: 9.486832981

Break this problem into two subproblems by setting 
(t + -8) equal to 9.486832981 and -9.486832981.


Subproblem 1
t + -8 = 9.486832981

Simplifying
t + -8 = 9.486832981

Reorder the terms:
-8 + t = 9.486832981

Solving
-8 + t = 9.486832981

Solving for variable 't'.

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

Add '8' to each side of the equation.
-8 + 8 + t = 9.486832981 + 8

Combine like terms: -8 + 8 = 0
0 + t = 9.486832981 + 8
t = 9.486832981 + 8

Combine like terms: 9.486832981 + 8 = 17.486832981
t = 17.486832981

Simplifying
t = 17.486832981


Subproblem 2
t + -8 = -9.486832981

Simplifying
t + -8 = -9.486832981

Reorder the terms:
-8 + t = -9.486832981

Solving
-8 + t = -9.486832981

Solving for variable 't'.

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

Add '8' to each side of the equation.
-8 + 8 + t = -9.486832981 + 8

Combine like terms: -8 + 8 = 0
0 + t = -9.486832981 + 8
t = -9.486832981 + 8

Combine like terms: -9.486832981 + 8 = -1.486832981
t = -1.486832981

Simplifying
t = -1.486832981


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {17.486832981, -1.486832981}
Solution
t = {17.486832981, -1.486832981}

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