-16t^2+28t+0.5=0

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Solution for -16t^2+28t+0.5=0 equation: 


Simplifying
-16t2 + 28t + 0.5 = 0

Reorder the terms:
0.5 + 28t + -16t2 = 0

Solving
0.5 + 28t + -16t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-0.03125 + -1.75t + t2 = 0

Move the constant term to the right:

Add '0.03125' to each side of the equation.
-0.03125 + -1.75t + 0.03125 + t2 = 0 + 0.03125

Reorder the terms:
-0.03125 + 0.03125 + -1.75t + t2 = 0 + 0.03125

Combine like terms: -0.03125 + 0.03125 = 0.00000
0.00000 + -1.75t + t2 = 0 + 0.03125
-1.75t + t2 = 0 + 0.03125

Combine like terms: 0 + 0.03125 = 0.03125
-1.75t + t2 = 0.03125

The t term is -1.75t.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75t + 0.765625 + t2 = 0.03125 + 0.765625

Reorder the terms:
0.765625 + -1.75t + t2 = 0.03125 + 0.765625

Combine like terms: 0.03125 + 0.765625 = 0.796875
0.765625 + -1.75t + t2 = 0.796875

Factor a perfect square on the left side:
(t + -0.875)(t + -0.875) = 0.796875

Calculate the square root of the right side: 0.892678554

Break this problem into two subproblems by setting 
(t + -0.875) equal to 0.892678554 and -0.892678554.


Subproblem 1
t + -0.875 = 0.892678554

Simplifying
t + -0.875 = 0.892678554

Reorder the terms:
-0.875 + t = 0.892678554

Solving
-0.875 + t = 0.892678554

Solving for variable 't'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + t = 0.892678554 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + t = 0.892678554 + 0.875
t = 0.892678554 + 0.875

Combine like terms: 0.892678554 + 0.875 = 1.767678554
t = 1.767678554

Simplifying
t = 1.767678554


Subproblem 2
t + -0.875 = -0.892678554

Simplifying
t + -0.875 = -0.892678554

Reorder the terms:
-0.875 + t = -0.892678554

Solving
-0.875 + t = -0.892678554

Solving for variable 't'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + t = -0.892678554 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + t = -0.892678554 + 0.875
t = -0.892678554 + 0.875

Combine like terms: -0.892678554 + 0.875 = -0.017678554
t = -0.017678554

Simplifying
t = -0.017678554


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.767678554, -0.017678554}

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