100t^2-1700t+2700=0

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Solution for 100t^2-1700t+2700=0 equation: 


Simplifying
100t2 + -1700t + 2700 = 0

Reorder the terms:
2700 + -1700t + 100t2 = 0

Solving
2700 + -1700t + 100t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '100'.
100(27 + -17t + t2) = 0

Ignore the factor 100.

Subproblem 1
Set the factor '(27 + -17t + t2)' equal to zero and attempt to solve:

Simplifying
27 + -17t + t2 = 0

Solving
27 + -17t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + -17t + -27 + t2 = 0 + -27

Reorder the terms:
27 + -27 + -17t + t2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -17t + t2 = 0 + -27
-17t + t2 = 0 + -27

Combine like terms: 0 + -27 = -27
-17t + t2 = -27

The t term is -17t.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17t + 72.25 + t2 = -27 + 72.25

Reorder the terms:
72.25 + -17t + t2 = -27 + 72.25

Combine like terms: -27 + 72.25 = 45.25
72.25 + -17t + t2 = 45.25

Factor a perfect square on the left side:
(t + -8.5)(t + -8.5) = 45.25

Calculate the square root of the right side: 6.726812024

Break this problem into two subproblems by setting 
(t + -8.5) equal to 6.726812024 and -6.726812024.


Subproblem 1
t + -8.5 = 6.726812024

Simplifying
t + -8.5 = 6.726812024

Reorder the terms:
-8.5 + t = 6.726812024

Solving
-8.5 + t = 6.726812024

Solving for variable 't'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + t = 6.726812024 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + t = 6.726812024 + 8.5
t = 6.726812024 + 8.5

Combine like terms: 6.726812024 + 8.5 = 15.226812024
t = 15.226812024

Simplifying
t = 15.226812024


Subproblem 2
t + -8.5 = -6.726812024

Simplifying
t + -8.5 = -6.726812024

Reorder the terms:
-8.5 + t = -6.726812024

Solving
-8.5 + t = -6.726812024

Solving for variable 't'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + t = -6.726812024 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + t = -6.726812024 + 8.5
t = -6.726812024 + 8.5

Combine like terms: -6.726812024 + 8.5 = 1.773187976
t = 1.773187976

Simplifying
t = 1.773187976


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {15.226812024, 1.773187976}
Solution
t = {15.226812024, 1.773187976}

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