16t^2+100t-75=0

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Solution for 16t^2+100t-75=0 equation: 


Simplifying
16t2 + 100t + -75 = 0

Reorder the terms:
-75 + 100t + 16t2 = 0

Solving
-75 + 100t + 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'.
-4.6875 + 6.25t + t2 = 0

Move the constant term to the right:

Add '4.6875' to each side of the equation.
-4.6875 + 6.25t + 4.6875 + t2 = 0 + 4.6875

Reorder the terms:
-4.6875 + 4.6875 + 6.25t + t2 = 0 + 4.6875

Combine like terms: -4.6875 + 4.6875 = 0.0000
0.0000 + 6.25t + t2 = 0 + 4.6875
6.25t + t2 = 0 + 4.6875

Combine like terms: 0 + 4.6875 = 4.6875
6.25t + t2 = 4.6875

The t term is 6.25t.  Take half its coefficient (3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
6.25t + 9.765625 + t2 = 4.6875 + 9.765625

Reorder the terms:
9.765625 + 6.25t + t2 = 4.6875 + 9.765625

Combine like terms: 4.6875 + 9.765625 = 14.453125
9.765625 + 6.25t + t2 = 14.453125

Factor a perfect square on the left side:
(t + 3.125)(t + 3.125) = 14.453125

Calculate the square root of the right side: 3.801726581

Break this problem into two subproblems by setting 
(t + 3.125) equal to 3.801726581 and -3.801726581.


Subproblem 1
t + 3.125 = 3.801726581

Simplifying
t + 3.125 = 3.801726581

Reorder the terms:
3.125 + t = 3.801726581

Solving
3.125 + t = 3.801726581

Solving for variable 't'.

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

Add '-3.125' to each side of the equation.
3.125 + -3.125 + t = 3.801726581 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + t = 3.801726581 + -3.125
t = 3.801726581 + -3.125

Combine like terms: 3.801726581 + -3.125 = 0.676726581
t = 0.676726581

Simplifying
t = 0.676726581


Subproblem 2
t + 3.125 = -3.801726581

Simplifying
t + 3.125 = -3.801726581

Reorder the terms:
3.125 + t = -3.801726581

Solving
3.125 + t = -3.801726581

Solving for variable 't'.

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

Add '-3.125' to each side of the equation.
3.125 + -3.125 + t = -3.801726581 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + t = -3.801726581 + -3.125
t = -3.801726581 + -3.125

Combine like terms: -3.801726581 + -3.125 = -6.926726581
t = -6.926726581

Simplifying
t = -6.926726581


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.676726581, -6.926726581}

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