-16t^2+28t-4=0

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Solution for -16t^2+28t-4=0 equation: 


Simplifying
-16t2 + 28t + -4 = 0

Reorder the terms:
-4 + 28t + -16t2 = 0

Solving
-4 + 28t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 7t + -4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-1 + 7t + -4t2)' equal to zero and attempt to solve:

Simplifying
-1 + 7t + -4t2 = 0

Solving
-1 + 7t + -4t2 = 0

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

Divide each side by '-4'.
0.25 + -1.75t + t2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -1.75t + -0.25 + t2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -1.75t + t2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -1.75t + t2 = 0 + -0.25
-1.75t + t2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-1.75t + t2 = -0.25

The t term is -1.75t.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75t + 0.765625 + t2 = -0.25 + 0.765625

Reorder the terms:
0.765625 + -1.75t + t2 = -0.25 + 0.765625

Combine like terms: -0.25 + 0.765625 = 0.515625
0.765625 + -1.75t + t2 = 0.515625

Factor a perfect square on the left side:
(t + -0.875)(t + -0.875) = 0.515625

Calculate the square root of the right side: 0.718070331

Break this problem into two subproblems by setting 
(t + -0.875) equal to 0.718070331 and -0.718070331.


Subproblem 1
t + -0.875 = 0.718070331

Simplifying
t + -0.875 = 0.718070331

Reorder the terms:
-0.875 + t = 0.718070331

Solving
-0.875 + t = 0.718070331

Solving for variable 't'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + t = 0.718070331 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + t = 0.718070331 + 0.875
t = 0.718070331 + 0.875

Combine like terms: 0.718070331 + 0.875 = 1.593070331
t = 1.593070331

Simplifying
t = 1.593070331


Subproblem 2
t + -0.875 = -0.718070331

Simplifying
t + -0.875 = -0.718070331

Reorder the terms:
-0.875 + t = -0.718070331

Solving
-0.875 + t = -0.718070331

Solving for variable 't'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + t = -0.718070331 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + t = -0.718070331 + 0.875
t = -0.718070331 + 0.875

Combine like terms: -0.718070331 + 0.875 = 0.156929669
t = 0.156929669

Simplifying
t = 0.156929669


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.593070331, 0.156929669}
Solution
t = {1.593070331, 0.156929669}

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