16t^2+36t-8=0

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Solution for 16t^2+36t-8=0 equation:


Simplifying
16t2 + 36t + -8 = 0

Reorder the terms:
-8 + 36t + 16t2 = 0

Solving
-8 + 36t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + 9t + 4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-2 + 9t + 4t2)' equal to zero and attempt to solve:

Simplifying
-2 + 9t + 4t2 = 0

Solving
-2 + 9t + 4t2 = 0

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

Divide each side by '4'.
-0.5 + 2.25t + t2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 2.25t + 0.5 + t2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 2.25t + t2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 2.25t + t2 = 0 + 0.5
2.25t + t2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
2.25t + t2 = 0.5

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 = 0.5 + 1.265625

Reorder the terms:
1.265625 + 2.25t + t2 = 0.5 + 1.265625

Combine like terms: 0.5 + 1.265625 = 1.765625
1.265625 + 2.25t + t2 = 1.765625

Factor a perfect square on the left side:
(t + 1.125)(t + 1.125) = 1.765625

Calculate the square root of the right side: 1.328768227

Break this problem into two subproblems by setting 
(t + 1.125) equal to 1.328768227 and -1.328768227.


Subproblem 1
t + 1.125 = 1.328768227

Simplifying
t + 1.125 = 1.328768227

Reorder the terms:
1.125 + t = 1.328768227

Solving
1.125 + t = 1.328768227

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 = 1.328768227 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + t = 1.328768227 + -1.125
t = 1.328768227 + -1.125

Combine like terms: 1.328768227 + -1.125 = 0.203768227
t = 0.203768227

Simplifying
t = 0.203768227


Subproblem 2
t + 1.125 = -1.328768227

Simplifying
t + 1.125 = -1.328768227

Reorder the terms:
1.125 + t = -1.328768227

Solving
1.125 + t = -1.328768227

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 = -1.328768227 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + t = -1.328768227 + -1.125
t = -1.328768227 + -1.125

Combine like terms: -1.328768227 + -1.125 = -2.453768227
t = -2.453768227

Simplifying
t = -2.453768227


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.203768227, -2.453768227}
Solution
t = {0.203768227, -2.453768227}

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