-16t^2+56t+18=0

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Solution for -16t^2+56t+18=0 equation: 


Simplifying
-16t2 + 56t + 18 = 0

Reorder the terms:
18 + 56t + -16t2 = 0

Solving
18 + 56t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 28t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(9 + 28t + -8t2)' equal to zero and attempt to solve:

Simplifying
9 + 28t + -8t2 = 0

Solving
9 + 28t + -8t2 = 0

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

Divide each side by '-8'.
-1.125 + -3.5t + t2 = 0

Move the constant term to the right:

Add '1.125' to each side of the equation.
-1.125 + -3.5t + 1.125 + t2 = 0 + 1.125

Reorder the terms:
-1.125 + 1.125 + -3.5t + t2 = 0 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + -3.5t + t2 = 0 + 1.125
-3.5t + t2 = 0 + 1.125

Combine like terms: 0 + 1.125 = 1.125
-3.5t + t2 = 1.125

The t term is -3.5t.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5t + 3.0625 + t2 = 1.125 + 3.0625

Reorder the terms:
3.0625 + -3.5t + t2 = 1.125 + 3.0625

Combine like terms: 1.125 + 3.0625 = 4.1875
3.0625 + -3.5t + t2 = 4.1875

Factor a perfect square on the left side:
(t + -1.75)(t + -1.75) = 4.1875

Calculate the square root of the right side: 2.046338193

Break this problem into two subproblems by setting 
(t + -1.75) equal to 2.046338193 and -2.046338193.


Subproblem 1
t + -1.75 = 2.046338193

Simplifying
t + -1.75 = 2.046338193

Reorder the terms:
-1.75 + t = 2.046338193

Solving
-1.75 + t = 2.046338193

Solving for variable 't'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + t = 2.046338193 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + t = 2.046338193 + 1.75
t = 2.046338193 + 1.75

Combine like terms: 2.046338193 + 1.75 = 3.796338193
t = 3.796338193

Simplifying
t = 3.796338193


Subproblem 2
t + -1.75 = -2.046338193

Simplifying
t + -1.75 = -2.046338193

Reorder the terms:
-1.75 + t = -2.046338193

Solving
-1.75 + t = -2.046338193

Solving for variable 't'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + t = -2.046338193 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + t = -2.046338193 + 1.75
t = -2.046338193 + 1.75

Combine like terms: -2.046338193 + 1.75 = -0.296338193
t = -0.296338193

Simplifying
t = -0.296338193


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.796338193, -0.296338193}
Solution
t = {3.796338193, -0.296338193}

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