-(16*t^2)+10*t+10=0

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Solution for -(16*t^2)+10*t+10=0 equation: 


Simplifying
-1(16t2) + 10t + 10 = 0

Remove parenthesis around (16t2)
-1 * 16t2 + 10t + 10 = 0

Multiply -1 * 16
-16t2 + 10t + 10 = 0

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

Solving
10 + 10t + -16t2 = 0

Solving for variable 't'.

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

Ignore the factor 2.

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

Simplifying
5 + 5t + -8t2 = 0

Solving
5 + 5t + -8t2 = 0

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

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

Move the constant term to the right:

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

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

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

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

The t term is -0.625t.  Take half its coefficient (-0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
-0.625t + 0.09765625 + t2 = 0.625 + 0.09765625

Reorder the terms:
0.09765625 + -0.625t + t2 = 0.625 + 0.09765625

Combine like terms: 0.625 + 0.09765625 = 0.72265625
0.09765625 + -0.625t + t2 = 0.72265625

Factor a perfect square on the left side:
(t + -0.3125)(t + -0.3125) = 0.72265625

Calculate the square root of the right side: 0.850091907

Break this problem into two subproblems by setting 
(t + -0.3125) equal to 0.850091907 and -0.850091907.


Subproblem 1
t + -0.3125 = 0.850091907

Simplifying
t + -0.3125 = 0.850091907

Reorder the terms:
-0.3125 + t = 0.850091907

Solving
-0.3125 + t = 0.850091907

Solving for variable 't'.

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

Add '0.3125' to each side of the equation.
-0.3125 + 0.3125 + t = 0.850091907 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + t = 0.850091907 + 0.3125
t = 0.850091907 + 0.3125

Combine like terms: 0.850091907 + 0.3125 = 1.162591907
t = 1.162591907

Simplifying
t = 1.162591907


Subproblem 2
t + -0.3125 = -0.850091907

Simplifying
t + -0.3125 = -0.850091907

Reorder the terms:
-0.3125 + t = -0.850091907

Solving
-0.3125 + t = -0.850091907

Solving for variable 't'.

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

Add '0.3125' to each side of the equation.
-0.3125 + 0.3125 + t = -0.850091907 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + t = -0.850091907 + 0.3125
t = -0.850091907 + 0.3125

Combine like terms: -0.850091907 + 0.3125 = -0.537591907
t = -0.537591907

Simplifying
t = -0.537591907


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.162591907, -0.537591907}
Solution
t = {1.162591907, -0.537591907}

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