5t^2-50t-40=0

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Solution for 5t^2-50t-40=0 equation: 


Simplifying
5t2 + -50t + -40 = 0

Reorder the terms:
-40 + -50t + 5t2 = 0

Solving
-40 + -50t + 5t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-8 + -10t + t2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-8 + -10t + t2)' equal to zero and attempt to solve:

Simplifying
-8 + -10t + t2 = 0

Solving
-8 + -10t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -10t + 8 + t2 = 0 + 8

Reorder the terms:
-8 + 8 + -10t + t2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -10t + t2 = 0 + 8
-10t + t2 = 0 + 8

Combine like terms: 0 + 8 = 8
-10t + t2 = 8

The t term is -10t.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10t + 25 + t2 = 8 + 25

Reorder the terms:
25 + -10t + t2 = 8 + 25

Combine like terms: 8 + 25 = 33
25 + -10t + t2 = 33

Factor a perfect square on the left side:
(t + -5)(t + -5) = 33

Calculate the square root of the right side: 5.744562647

Break this problem into two subproblems by setting 
(t + -5) equal to 5.744562647 and -5.744562647.


Subproblem 1
t + -5 = 5.744562647

Simplifying
t + -5 = 5.744562647

Reorder the terms:
-5 + t = 5.744562647

Solving
-5 + t = 5.744562647

Solving for variable 't'.

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

Add '5' to each side of the equation.
-5 + 5 + t = 5.744562647 + 5

Combine like terms: -5 + 5 = 0
0 + t = 5.744562647 + 5
t = 5.744562647 + 5

Combine like terms: 5.744562647 + 5 = 10.744562647
t = 10.744562647

Simplifying
t = 10.744562647


Subproblem 2
t + -5 = -5.744562647

Simplifying
t + -5 = -5.744562647

Reorder the terms:
-5 + t = -5.744562647

Solving
-5 + t = -5.744562647

Solving for variable 't'.

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

Add '5' to each side of the equation.
-5 + 5 + t = -5.744562647 + 5

Combine like terms: -5 + 5 = 0
0 + t = -5.744562647 + 5
t = -5.744562647 + 5

Combine like terms: -5.744562647 + 5 = -0.744562647
t = -0.744562647

Simplifying
t = -0.744562647


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {10.744562647, -0.744562647}
Solution
t = {10.744562647, -0.744562647}

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