-16t^2+235t-151=0

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Solution for -16t^2+235t-151=0 equation: 


Simplifying
-16t2 + 235t + -151 = 0

Reorder the terms:
-151 + 235t + -16t2 = 0

Solving
-151 + 235t + -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'.
9.4375 + -14.6875t + t2 = 0

Move the constant term to the right:

Add '-9.4375' to each side of the equation.
9.4375 + -14.6875t + -9.4375 + t2 = 0 + -9.4375

Reorder the terms:
9.4375 + -9.4375 + -14.6875t + t2 = 0 + -9.4375

Combine like terms: 9.4375 + -9.4375 = 0.0000
0.0000 + -14.6875t + t2 = 0 + -9.4375
-14.6875t + t2 = 0 + -9.4375

Combine like terms: 0 + -9.4375 = -9.4375
-14.6875t + t2 = -9.4375

The t term is -14.6875t.  Take half its coefficient (-7.34375).
Square it (53.93066406) and add it to both sides.

Add '53.93066406' to each side of the equation.
-14.6875t + 53.93066406 + t2 = -9.4375 + 53.93066406

Reorder the terms:
53.93066406 + -14.6875t + t2 = -9.4375 + 53.93066406

Combine like terms: -9.4375 + 53.93066406 = 44.49316406
53.93066406 + -14.6875t + t2 = 44.49316406

Factor a perfect square on the left side:
(t + -7.34375)(t + -7.34375) = 44.49316406

Calculate the square root of the right side: 6.670319637

Break this problem into two subproblems by setting 
(t + -7.34375) equal to 6.670319637 and -6.670319637.


Subproblem 1
t + -7.34375 = 6.670319637

Simplifying
t + -7.34375 = 6.670319637

Reorder the terms:
-7.34375 + t = 6.670319637

Solving
-7.34375 + t = 6.670319637

Solving for variable 't'.

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

Add '7.34375' to each side of the equation.
-7.34375 + 7.34375 + t = 6.670319637 + 7.34375

Combine like terms: -7.34375 + 7.34375 = 0.00000
0.00000 + t = 6.670319637 + 7.34375
t = 6.670319637 + 7.34375

Combine like terms: 6.670319637 + 7.34375 = 14.014069637
t = 14.014069637

Simplifying
t = 14.014069637


Subproblem 2
t + -7.34375 = -6.670319637

Simplifying
t + -7.34375 = -6.670319637

Reorder the terms:
-7.34375 + t = -6.670319637

Solving
-7.34375 + t = -6.670319637

Solving for variable 't'.

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

Add '7.34375' to each side of the equation.
-7.34375 + 7.34375 + t = -6.670319637 + 7.34375

Combine like terms: -7.34375 + 7.34375 = 0.00000
0.00000 + t = -6.670319637 + 7.34375
t = -6.670319637 + 7.34375

Combine like terms: -6.670319637 + 7.34375 = 0.673430363
t = 0.673430363

Simplifying
t = 0.673430363


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {14.014069637, 0.673430363}

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