5t^2-40t-10=0

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Solution for 5t^2-40t-10=0 equation: 


Simplifying
5t2 + -40t + -10 = 0

Reorder the terms:
-10 + -40t + 5t2 = 0

Solving
-10 + -40t + 5t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-2 + -8t + t2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-2 + -8t + t2)' equal to zero and attempt to solve:

Simplifying
-2 + -8t + t2 = 0

Solving
-2 + -8t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -8t + 2 + t2 = 0 + 2

Reorder the terms:
-2 + 2 + -8t + t2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -8t + t2 = 0 + 2
-8t + t2 = 0 + 2

Combine like terms: 0 + 2 = 2
-8t + t2 = 2

The t term is -8t.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8t + 16 + t2 = 2 + 16

Reorder the terms:
16 + -8t + t2 = 2 + 16

Combine like terms: 2 + 16 = 18
16 + -8t + t2 = 18

Factor a perfect square on the left side:
(t + -4)(t + -4) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(t + -4) equal to 4.242640687 and -4.242640687.


Subproblem 1
t + -4 = 4.242640687

Simplifying
t + -4 = 4.242640687

Reorder the terms:
-4 + t = 4.242640687

Solving
-4 + t = 4.242640687

Solving for variable 't'.

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

Add '4' to each side of the equation.
-4 + 4 + t = 4.242640687 + 4

Combine like terms: -4 + 4 = 0
0 + t = 4.242640687 + 4
t = 4.242640687 + 4

Combine like terms: 4.242640687 + 4 = 8.242640687
t = 8.242640687

Simplifying
t = 8.242640687


Subproblem 2
t + -4 = -4.242640687

Simplifying
t + -4 = -4.242640687

Reorder the terms:
-4 + t = -4.242640687

Solving
-4 + t = -4.242640687

Solving for variable 't'.

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

Add '4' to each side of the equation.
-4 + 4 + t = -4.242640687 + 4

Combine like terms: -4 + 4 = 0
0 + t = -4.242640687 + 4
t = -4.242640687 + 4

Combine like terms: -4.242640687 + 4 = -0.242640687
t = -0.242640687

Simplifying
t = -0.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {8.242640687, -0.242640687}
Solution
t = {8.242640687, -0.242640687}

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