8t^2-100t-1000=0

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Solution for 8t^2-100t-1000=0 equation: 


Simplifying
8t2 + -100t + -1000 = 0

Reorder the terms:
-1000 + -100t + 8t2 = 0

Solving
-1000 + -100t + 8t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-250 + -25t + 2t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-250 + -25t + 2t2)' equal to zero and attempt to solve:

Simplifying
-250 + -25t + 2t2 = 0

Solving
-250 + -25t + 2t2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-125 + -12.5t + t2 = 0

Move the constant term to the right:

Add '125' to each side of the equation.
-125 + -12.5t + 125 + t2 = 0 + 125

Reorder the terms:
-125 + 125 + -12.5t + t2 = 0 + 125

Combine like terms: -125 + 125 = 0
0 + -12.5t + t2 = 0 + 125
-12.5t + t2 = 0 + 125

Combine like terms: 0 + 125 = 125
-12.5t + t2 = 125

The t term is -12.5t.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5t + 39.0625 + t2 = 125 + 39.0625

Reorder the terms:
39.0625 + -12.5t + t2 = 125 + 39.0625

Combine like terms: 125 + 39.0625 = 164.0625
39.0625 + -12.5t + t2 = 164.0625

Factor a perfect square on the left side:
(t + -6.25)(t + -6.25) = 164.0625

Calculate the square root of the right side: 12.808688457

Break this problem into two subproblems by setting 
(t + -6.25) equal to 12.808688457 and -12.808688457.


Subproblem 1
t + -6.25 = 12.808688457

Simplifying
t + -6.25 = 12.808688457

Reorder the terms:
-6.25 + t = 12.808688457

Solving
-6.25 + t = 12.808688457

Solving for variable 't'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + t = 12.808688457 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + t = 12.808688457 + 6.25
t = 12.808688457 + 6.25

Combine like terms: 12.808688457 + 6.25 = 19.058688457
t = 19.058688457

Simplifying
t = 19.058688457


Subproblem 2
t + -6.25 = -12.808688457

Simplifying
t + -6.25 = -12.808688457

Reorder the terms:
-6.25 + t = -12.808688457

Solving
-6.25 + t = -12.808688457

Solving for variable 't'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + t = -12.808688457 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + t = -12.808688457 + 6.25
t = -12.808688457 + 6.25

Combine like terms: -12.808688457 + 6.25 = -6.558688457
t = -6.558688457

Simplifying
t = -6.558688457


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {19.058688457, -6.558688457}
Solution
t = {19.058688457, -6.558688457}

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