-16t^2+36t-10=0

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Solution for -16t^2+36t-10=0 equation: 


Simplifying
-16t2 + 36t + -10 = 0

Reorder the terms:
-10 + 36t + -16t2 = 0

Solving
-10 + 36t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 18t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 18t + -8t2)' equal to zero and attempt to solve:

Simplifying
-5 + 18t + -8t2 = 0

Solving
-5 + 18t + -8t2 = 0

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

Divide each side by '-8'.
0.625 + -2.25t + t2 = 0

Move the constant term to the right:

Add '-0.625' to each side of the equation.
0.625 + -2.25t + -0.625 + t2 = 0 + -0.625

Reorder the terms:
0.625 + -0.625 + -2.25t + t2 = 0 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + -2.25t + t2 = 0 + -0.625
-2.25t + t2 = 0 + -0.625

Combine like terms: 0 + -0.625 = -0.625
-2.25t + t2 = -0.625

The t term is -2.25t.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25t + 1.265625 + t2 = -0.625 + 1.265625

Reorder the terms:
1.265625 + -2.25t + t2 = -0.625 + 1.265625

Combine like terms: -0.625 + 1.265625 = 0.640625
1.265625 + -2.25t + t2 = 0.640625

Factor a perfect square on the left side:
(t + -1.125)(t + -1.125) = 0.640625

Calculate the square root of the right side: 0.80039053

Break this problem into two subproblems by setting 
(t + -1.125) equal to 0.80039053 and -0.80039053.


Subproblem 1
t + -1.125 = 0.80039053

Simplifying
t + -1.125 = 0.80039053

Reorder the terms:
-1.125 + t = 0.80039053

Solving
-1.125 + t = 0.80039053

Solving for variable 't'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + t = 0.80039053 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + t = 0.80039053 + 1.125
t = 0.80039053 + 1.125

Combine like terms: 0.80039053 + 1.125 = 1.92539053
t = 1.92539053

Simplifying
t = 1.92539053


Subproblem 2
t + -1.125 = -0.80039053

Simplifying
t + -1.125 = -0.80039053

Reorder the terms:
-1.125 + t = -0.80039053

Solving
-1.125 + t = -0.80039053

Solving for variable 't'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + t = -0.80039053 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + t = -0.80039053 + 1.125
t = -0.80039053 + 1.125

Combine like terms: -0.80039053 + 1.125 = 0.32460947
t = 0.32460947

Simplifying
t = 0.32460947


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.92539053, 0.32460947}
Solution
t = {1.92539053, 0.32460947}

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