5t^2-5t-40=0

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Solution for 5t^2-5t-40=0 equation: 


Simplifying
5t2 + -5t + -40 = 0

Reorder the terms:
-40 + -5t + 5t2 = 0

Solving
-40 + -5t + 5t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-8 + -1t + t2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-8 + -1t + t2)' equal to zero and attempt to solve:

Simplifying
-8 + -1t + t2 = 0

Solving
-8 + -1t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -1t + 8 + t2 = 0 + 8

Reorder the terms:
-8 + 8 + -1t + t2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1t + t2 = 0 + 8
-1t + t2 = 0 + 8

Combine like terms: 0 + 8 = 8
-1t + t2 = 8

The t term is -1t.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1t + 0.25 + t2 = 8 + 0.25

Reorder the terms:
0.25 + -1t + t2 = 8 + 0.25

Combine like terms: 8 + 0.25 = 8.25
0.25 + -1t + t2 = 8.25

Factor a perfect square on the left side:
(t + -0.5)(t + -0.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(t + -0.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
t + -0.5 = 2.872281323

Simplifying
t + -0.5 = 2.872281323

Reorder the terms:
-0.5 + t = 2.872281323

Solving
-0.5 + t = 2.872281323

Solving for variable 't'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + t = 2.872281323 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + t = 2.872281323 + 0.5
t = 2.872281323 + 0.5

Combine like terms: 2.872281323 + 0.5 = 3.372281323
t = 3.372281323

Simplifying
t = 3.372281323


Subproblem 2
t + -0.5 = -2.872281323

Simplifying
t + -0.5 = -2.872281323

Reorder the terms:
-0.5 + t = -2.872281323

Solving
-0.5 + t = -2.872281323

Solving for variable 't'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + t = -2.872281323 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + t = -2.872281323 + 0.5
t = -2.872281323 + 0.5

Combine like terms: -2.872281323 + 0.5 = -2.372281323
t = -2.372281323

Simplifying
t = -2.372281323


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.372281323, -2.372281323}
Solution
t = {3.372281323, -2.372281323}

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