16t^2+68t-100=0

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Solution for 16t^2+68t-100=0 equation: 


Simplifying
16t2 + 68t + -100 = 0

Reorder the terms:
-100 + 68t + 16t2 = 0

Solving
-100 + 68t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-25 + 17t + 4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-25 + 17t + 4t2)' equal to zero and attempt to solve:

Simplifying
-25 + 17t + 4t2 = 0

Solving
-25 + 17t + 4t2 = 0

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

Divide each side by '4'.
-6.25 + 4.25t + t2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + 4.25t + 6.25 + t2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + 4.25t + t2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + 4.25t + t2 = 0 + 6.25
4.25t + t2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
4.25t + t2 = 6.25

The t term is 4.25t.  Take half its coefficient (2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
4.25t + 4.515625 + t2 = 6.25 + 4.515625

Reorder the terms:
4.515625 + 4.25t + t2 = 6.25 + 4.515625

Combine like terms: 6.25 + 4.515625 = 10.765625
4.515625 + 4.25t + t2 = 10.765625

Factor a perfect square on the left side:
(t + 2.125)(t + 2.125) = 10.765625

Calculate the square root of the right side: 3.281101187

Break this problem into two subproblems by setting 
(t + 2.125) equal to 3.281101187 and -3.281101187.


Subproblem 1
t + 2.125 = 3.281101187

Simplifying
t + 2.125 = 3.281101187

Reorder the terms:
2.125 + t = 3.281101187

Solving
2.125 + t = 3.281101187

Solving for variable 't'.

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

Add '-2.125' to each side of the equation.
2.125 + -2.125 + t = 3.281101187 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + t = 3.281101187 + -2.125
t = 3.281101187 + -2.125

Combine like terms: 3.281101187 + -2.125 = 1.156101187
t = 1.156101187

Simplifying
t = 1.156101187


Subproblem 2
t + 2.125 = -3.281101187

Simplifying
t + 2.125 = -3.281101187

Reorder the terms:
2.125 + t = -3.281101187

Solving
2.125 + t = -3.281101187

Solving for variable 't'.

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

Add '-2.125' to each side of the equation.
2.125 + -2.125 + t = -3.281101187 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + t = -3.281101187 + -2.125
t = -3.281101187 + -2.125

Combine like terms: -3.281101187 + -2.125 = -5.406101187
t = -5.406101187

Simplifying
t = -5.406101187


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.156101187, -5.406101187}
Solution
t = {1.156101187, -5.406101187}

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