5t^2-80t-245=0

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Solution for 5t^2-80t-245=0 equation: 


Simplifying
5t2 + -80t + -245 = 0

Reorder the terms:
-245 + -80t + 5t2 = 0

Solving
-245 + -80t + 5t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-49 + -16t + t2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-49 + -16t + t2)' equal to zero and attempt to solve:

Simplifying
-49 + -16t + t2 = 0

Solving
-49 + -16t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + -16t + 49 + t2 = 0 + 49

Reorder the terms:
-49 + 49 + -16t + t2 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + -16t + t2 = 0 + 49
-16t + t2 = 0 + 49

Combine like terms: 0 + 49 = 49
-16t + t2 = 49

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 = 49 + 64

Reorder the terms:
64 + -16t + t2 = 49 + 64

Combine like terms: 49 + 64 = 113
64 + -16t + t2 = 113

Factor a perfect square on the left side:
(t + -8)(t + -8) = 113

Calculate the square root of the right side: 10.630145813

Break this problem into two subproblems by setting 
(t + -8) equal to 10.630145813 and -10.630145813.


Subproblem 1
t + -8 = 10.630145813

Simplifying
t + -8 = 10.630145813

Reorder the terms:
-8 + t = 10.630145813

Solving
-8 + t = 10.630145813

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 = 10.630145813 + 8

Combine like terms: -8 + 8 = 0
0 + t = 10.630145813 + 8
t = 10.630145813 + 8

Combine like terms: 10.630145813 + 8 = 18.630145813
t = 18.630145813

Simplifying
t = 18.630145813


Subproblem 2
t + -8 = -10.630145813

Simplifying
t + -8 = -10.630145813

Reorder the terms:
-8 + t = -10.630145813

Solving
-8 + t = -10.630145813

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 = -10.630145813 + 8

Combine like terms: -8 + 8 = 0
0 + t = -10.630145813 + 8
t = -10.630145813 + 8

Combine like terms: -10.630145813 + 8 = -2.630145813
t = -2.630145813

Simplifying
t = -2.630145813


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {18.630145813, -2.630145813}
Solution
t = {18.630145813, -2.630145813}

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