-16t^2-2t+400=0

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Solution for -16t^2-2t+400=0 equation: 


Simplifying
-16t2 + -2t + 400 = 0

Reorder the terms:
400 + -2t + -16t2 = 0

Solving
400 + -2t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(200 + -1t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(200 + -1t + -8t2)' equal to zero and attempt to solve:

Simplifying
200 + -1t + -8t2 = 0

Solving
200 + -1t + -8t2 = 0

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

Divide each side by '-8'.
-25 + 0.125t + t2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 0.125t + 25 + t2 = 0 + 25

Reorder the terms:
-25 + 25 + 0.125t + t2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 0.125t + t2 = 0 + 25
0.125t + t2 = 0 + 25

Combine like terms: 0 + 25 = 25
0.125t + t2 = 25

The t term is 0.125t.  Take half its coefficient (0.0625).
Square it (0.00390625) and add it to both sides.

Add '0.00390625' to each side of the equation.
0.125t + 0.00390625 + t2 = 25 + 0.00390625

Reorder the terms:
0.00390625 + 0.125t + t2 = 25 + 0.00390625

Combine like terms: 25 + 0.00390625 = 25.00390625
0.00390625 + 0.125t + t2 = 25.00390625

Factor a perfect square on the left side:
(t + 0.0625)(t + 0.0625) = 25.00390625

Calculate the square root of the right side: 5.00039061

Break this problem into two subproblems by setting 
(t + 0.0625) equal to 5.00039061 and -5.00039061.


Subproblem 1
t + 0.0625 = 5.00039061

Simplifying
t + 0.0625 = 5.00039061

Reorder the terms:
0.0625 + t = 5.00039061

Solving
0.0625 + t = 5.00039061

Solving for variable 't'.

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

Add '-0.0625' to each side of the equation.
0.0625 + -0.0625 + t = 5.00039061 + -0.0625

Combine like terms: 0.0625 + -0.0625 = 0.0000
0.0000 + t = 5.00039061 + -0.0625
t = 5.00039061 + -0.0625

Combine like terms: 5.00039061 + -0.0625 = 4.93789061
t = 4.93789061

Simplifying
t = 4.93789061


Subproblem 2
t + 0.0625 = -5.00039061

Simplifying
t + 0.0625 = -5.00039061

Reorder the terms:
0.0625 + t = -5.00039061

Solving
0.0625 + t = -5.00039061

Solving for variable 't'.

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

Add '-0.0625' to each side of the equation.
0.0625 + -0.0625 + t = -5.00039061 + -0.0625

Combine like terms: 0.0625 + -0.0625 = 0.0000
0.0000 + t = -5.00039061 + -0.0625
t = -5.00039061 + -0.0625

Combine like terms: -5.00039061 + -0.0625 = -5.06289061
t = -5.06289061

Simplifying
t = -5.06289061


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.93789061, -5.06289061}
Solution
t = {4.93789061, -5.06289061}

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