80*t^2-250*t-150=0

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Solution for 80*t^2-250*t-150=0 equation:


Simplifying
80t2 + -250t + -150 = 0

Reorder the terms:
-150 + -250t + 80t2 = 0

Solving
-150 + -250t + 80t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-15 + -25t + 8t2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-15 + -25t + 8t2)' equal to zero and attempt to solve:

Simplifying
-15 + -25t + 8t2 = 0

Solving
-15 + -25t + 8t2 = 0

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

Divide each side by '8'.
-1.875 + -3.125t + t2 = 0

Move the constant term to the right:

Add '1.875' to each side of the equation.
-1.875 + -3.125t + 1.875 + t2 = 0 + 1.875

Reorder the terms:
-1.875 + 1.875 + -3.125t + t2 = 0 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + -3.125t + t2 = 0 + 1.875
-3.125t + t2 = 0 + 1.875

Combine like terms: 0 + 1.875 = 1.875
-3.125t + t2 = 1.875

The t term is -3.125t.  Take half its coefficient (-1.5625).
Square it (2.44140625) and add it to both sides.

Add '2.44140625' to each side of the equation.
-3.125t + 2.44140625 + t2 = 1.875 + 2.44140625

Reorder the terms:
2.44140625 + -3.125t + t2 = 1.875 + 2.44140625

Combine like terms: 1.875 + 2.44140625 = 4.31640625
2.44140625 + -3.125t + t2 = 4.31640625

Factor a perfect square on the left side:
(t + -1.5625)(t + -1.5625) = 4.31640625

Calculate the square root of the right side: 2.077596267

Break this problem into two subproblems by setting 
(t + -1.5625) equal to 2.077596267 and -2.077596267.


Subproblem 1
t + -1.5625 = 2.077596267

Simplifying
t + -1.5625 = 2.077596267

Reorder the terms:
-1.5625 + t = 2.077596267

Solving
-1.5625 + t = 2.077596267

Solving for variable 't'.

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

Add '1.5625' to each side of the equation.
-1.5625 + 1.5625 + t = 2.077596267 + 1.5625

Combine like terms: -1.5625 + 1.5625 = 0.0000
0.0000 + t = 2.077596267 + 1.5625
t = 2.077596267 + 1.5625

Combine like terms: 2.077596267 + 1.5625 = 3.640096267
t = 3.640096267

Simplifying
t = 3.640096267


Subproblem 2
t + -1.5625 = -2.077596267

Simplifying
t + -1.5625 = -2.077596267

Reorder the terms:
-1.5625 + t = -2.077596267

Solving
-1.5625 + t = -2.077596267

Solving for variable 't'.

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

Add '1.5625' to each side of the equation.
-1.5625 + 1.5625 + t = -2.077596267 + 1.5625

Combine like terms: -1.5625 + 1.5625 = 0.0000
0.0000 + t = -2.077596267 + 1.5625
t = -2.077596267 + 1.5625

Combine like terms: -2.077596267 + 1.5625 = -0.515096267
t = -0.515096267

Simplifying
t = -0.515096267


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.640096267, -0.515096267}
Solution
t = {3.640096267, -0.515096267}

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