-16t^2+20t+10=0

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Solution for -16t^2+20t+10=0 equation: 


Simplifying
-16t2 + 20t + 10 = 0

Reorder the terms:
10 + 20t + -16t2 = 0

Solving
10 + 20t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 10t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + 10t + -8t2)' equal to zero and attempt to solve:

Simplifying
5 + 10t + -8t2 = 0

Solving
5 + 10t + -8t2 = 0

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

Divide each side by '-8'.
-0.625 + -1.25t + t2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + -1.25t + 0.625 + t2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + -1.25t + t2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + -1.25t + t2 = 0 + 0.625
-1.25t + t2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
-1.25t + t2 = 0.625

The t term is -1.25t.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25t + 0.390625 + t2 = 0.625 + 0.390625

Reorder the terms:
0.390625 + -1.25t + t2 = 0.625 + 0.390625

Combine like terms: 0.625 + 0.390625 = 1.015625
0.390625 + -1.25t + t2 = 1.015625

Factor a perfect square on the left side:
(t + -0.625)(t + -0.625) = 1.015625

Calculate the square root of the right side: 1.007782219

Break this problem into two subproblems by setting 
(t + -0.625) equal to 1.007782219 and -1.007782219.


Subproblem 1
t + -0.625 = 1.007782219

Simplifying
t + -0.625 = 1.007782219

Reorder the terms:
-0.625 + t = 1.007782219

Solving
-0.625 + t = 1.007782219

Solving for variable 't'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + t = 1.007782219 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + t = 1.007782219 + 0.625
t = 1.007782219 + 0.625

Combine like terms: 1.007782219 + 0.625 = 1.632782219
t = 1.632782219

Simplifying
t = 1.632782219


Subproblem 2
t + -0.625 = -1.007782219

Simplifying
t + -0.625 = -1.007782219

Reorder the terms:
-0.625 + t = -1.007782219

Solving
-0.625 + t = -1.007782219

Solving for variable 't'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + t = -1.007782219 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + t = -1.007782219 + 0.625
t = -1.007782219 + 0.625

Combine like terms: -1.007782219 + 0.625 = -0.382782219
t = -0.382782219

Simplifying
t = -0.382782219


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.632782219, -0.382782219}
Solution
t = {1.632782219, -0.382782219}

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