-16t^2+35t+1.5=0

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Solution for -16t^2+35t+1.5=0 equation: 


Simplifying
-16t2 + 35t + 1.5 = 0

Reorder the terms:
1.5 + 35t + -16t2 = 0

Solving
1.5 + 35t + -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'.
-0.09375 + -2.1875t + t2 = 0

Move the constant term to the right:

Add '0.09375' to each side of the equation.
-0.09375 + -2.1875t + 0.09375 + t2 = 0 + 0.09375

Reorder the terms:
-0.09375 + 0.09375 + -2.1875t + t2 = 0 + 0.09375

Combine like terms: -0.09375 + 0.09375 = 0.00000
0.00000 + -2.1875t + t2 = 0 + 0.09375
-2.1875t + t2 = 0 + 0.09375

Combine like terms: 0 + 0.09375 = 0.09375
-2.1875t + t2 = 0.09375

The t term is -2.1875t.  Take half its coefficient (-1.09375).
Square it (1.196289063) and add it to both sides.

Add '1.196289063' to each side of the equation.
-2.1875t + 1.196289063 + t2 = 0.09375 + 1.196289063

Reorder the terms:
1.196289063 + -2.1875t + t2 = 0.09375 + 1.196289063

Combine like terms: 0.09375 + 1.196289063 = 1.290039063
1.196289063 + -2.1875t + t2 = 1.290039063

Factor a perfect square on the left side:
(t + -1.09375)(t + -1.09375) = 1.290039063

Calculate the square root of the right side: 1.135798866

Break this problem into two subproblems by setting 
(t + -1.09375) equal to 1.135798866 and -1.135798866.


Subproblem 1
t + -1.09375 = 1.135798866

Simplifying
t + -1.09375 = 1.135798866

Reorder the terms:
-1.09375 + t = 1.135798866

Solving
-1.09375 + t = 1.135798866

Solving for variable 't'.

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

Add '1.09375' to each side of the equation.
-1.09375 + 1.09375 + t = 1.135798866 + 1.09375

Combine like terms: -1.09375 + 1.09375 = 0.00000
0.00000 + t = 1.135798866 + 1.09375
t = 1.135798866 + 1.09375

Combine like terms: 1.135798866 + 1.09375 = 2.229548866
t = 2.229548866

Simplifying
t = 2.229548866


Subproblem 2
t + -1.09375 = -1.135798866

Simplifying
t + -1.09375 = -1.135798866

Reorder the terms:
-1.09375 + t = -1.135798866

Solving
-1.09375 + t = -1.135798866

Solving for variable 't'.

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

Add '1.09375' to each side of the equation.
-1.09375 + 1.09375 + t = -1.135798866 + 1.09375

Combine like terms: -1.09375 + 1.09375 = 0.00000
0.00000 + t = -1.135798866 + 1.09375
t = -1.135798866 + 1.09375

Combine like terms: -1.135798866 + 1.09375 = -0.042048866
t = -0.042048866

Simplifying
t = -0.042048866


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.229548866, -0.042048866}

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