-16t^2-8t+10=0

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Solution for -16t^2-8t+10=0 equation: 


Simplifying
-16t2 + -8t + 10 = 0

Reorder the terms:
10 + -8t + -16t2 = 0

Solving
10 + -8t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -4t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -4t + -8t2)' equal to zero and attempt to solve:

Simplifying
5 + -4t + -8t2 = 0

Solving
5 + -4t + -8t2 = 0

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

Divide each side by '-8'.
-0.625 + 0.5t + t2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + 0.5t + 0.625 + t2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + 0.5t + t2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + 0.5t + t2 = 0 + 0.625
0.5t + t2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
0.5t + t2 = 0.625

The t term is 0.5t.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5t + 0.0625 + t2 = 0.625 + 0.0625

Reorder the terms:
0.0625 + 0.5t + t2 = 0.625 + 0.0625

Combine like terms: 0.625 + 0.0625 = 0.6875
0.0625 + 0.5t + t2 = 0.6875

Factor a perfect square on the left side:
(t + 0.25)(t + 0.25) = 0.6875

Calculate the square root of the right side: 0.829156198

Break this problem into two subproblems by setting 
(t + 0.25) equal to 0.829156198 and -0.829156198.


Subproblem 1
t + 0.25 = 0.829156198

Simplifying
t + 0.25 = 0.829156198

Reorder the terms:
0.25 + t = 0.829156198

Solving
0.25 + t = 0.829156198

Solving for variable 't'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + t = 0.829156198 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + t = 0.829156198 + -0.25
t = 0.829156198 + -0.25

Combine like terms: 0.829156198 + -0.25 = 0.579156198
t = 0.579156198

Simplifying
t = 0.579156198


Subproblem 2
t + 0.25 = -0.829156198

Simplifying
t + 0.25 = -0.829156198

Reorder the terms:
0.25 + t = -0.829156198

Solving
0.25 + t = -0.829156198

Solving for variable 't'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + t = -0.829156198 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + t = -0.829156198 + -0.25
t = -0.829156198 + -0.25

Combine like terms: -0.829156198 + -0.25 = -1.079156198
t = -1.079156198

Simplifying
t = -1.079156198


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.579156198, -1.079156198}
Solution
t = {0.579156198, -1.079156198}

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