-16t^2+80t-70=0

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Solution for -16t^2+80t-70=0 equation: 


Simplifying
-16t2 + 80t + -70 = 0

Reorder the terms:
-70 + 80t + -16t2 = 0

Solving
-70 + 80t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-35 + 40t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-35 + 40t + -8t2)' equal to zero and attempt to solve:

Simplifying
-35 + 40t + -8t2 = 0

Solving
-35 + 40t + -8t2 = 0

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

Divide each side by '-8'.
4.375 + -5t + t2 = 0

Move the constant term to the right:

Add '-4.375' to each side of the equation.
4.375 + -5t + -4.375 + t2 = 0 + -4.375

Reorder the terms:
4.375 + -4.375 + -5t + t2 = 0 + -4.375

Combine like terms: 4.375 + -4.375 = 0.000
0.000 + -5t + t2 = 0 + -4.375
-5t + t2 = 0 + -4.375

Combine like terms: 0 + -4.375 = -4.375
-5t + t2 = -4.375

The t term is -5t.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5t + 6.25 + t2 = -4.375 + 6.25

Reorder the terms:
6.25 + -5t + t2 = -4.375 + 6.25

Combine like terms: -4.375 + 6.25 = 1.875
6.25 + -5t + t2 = 1.875

Factor a perfect square on the left side:
(t + -2.5)(t + -2.5) = 1.875

Calculate the square root of the right side: 1.369306394

Break this problem into two subproblems by setting 
(t + -2.5) equal to 1.369306394 and -1.369306394.


Subproblem 1
t + -2.5 = 1.369306394

Simplifying
t + -2.5 = 1.369306394

Reorder the terms:
-2.5 + t = 1.369306394

Solving
-2.5 + t = 1.369306394

Solving for variable 't'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + t = 1.369306394 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = 1.369306394 + 2.5
t = 1.369306394 + 2.5

Combine like terms: 1.369306394 + 2.5 = 3.869306394
t = 3.869306394

Simplifying
t = 3.869306394


Subproblem 2
t + -2.5 = -1.369306394

Simplifying
t + -2.5 = -1.369306394

Reorder the terms:
-2.5 + t = -1.369306394

Solving
-2.5 + t = -1.369306394

Solving for variable 't'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + t = -1.369306394 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = -1.369306394 + 2.5
t = -1.369306394 + 2.5

Combine like terms: -1.369306394 + 2.5 = 1.130693606
t = 1.130693606

Simplifying
t = 1.130693606


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.869306394, 1.130693606}
Solution
t = {3.869306394, 1.130693606}

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