-16t^2+500t-700=0

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Solution for -16t^2+500t-700=0 equation: 


Simplifying
-16t2 + 500t + -700 = 0

Reorder the terms:
-700 + 500t + -16t2 = 0

Solving
-700 + 500t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-175 + 125t + -4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-175 + 125t + -4t2)' equal to zero and attempt to solve:

Simplifying
-175 + 125t + -4t2 = 0

Solving
-175 + 125t + -4t2 = 0

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

Divide each side by '-4'.
43.75 + -31.25t + t2 = 0

Move the constant term to the right:

Add '-43.75' to each side of the equation.
43.75 + -31.25t + -43.75 + t2 = 0 + -43.75

Reorder the terms:
43.75 + -43.75 + -31.25t + t2 = 0 + -43.75

Combine like terms: 43.75 + -43.75 = 0.00
0.00 + -31.25t + t2 = 0 + -43.75
-31.25t + t2 = 0 + -43.75

Combine like terms: 0 + -43.75 = -43.75
-31.25t + t2 = -43.75

The t term is -31.25t.  Take half its coefficient (-15.625).
Square it (244.140625) and add it to both sides.

Add '244.140625' to each side of the equation.
-31.25t + 244.140625 + t2 = -43.75 + 244.140625

Reorder the terms:
244.140625 + -31.25t + t2 = -43.75 + 244.140625

Combine like terms: -43.75 + 244.140625 = 200.390625
244.140625 + -31.25t + t2 = 200.390625

Factor a perfect square on the left side:
(t + -15.625)(t + -15.625) = 200.390625

Calculate the square root of the right side: 14.155939566

Break this problem into two subproblems by setting 
(t + -15.625) equal to 14.155939566 and -14.155939566.


Subproblem 1
t + -15.625 = 14.155939566

Simplifying
t + -15.625 = 14.155939566

Reorder the terms:
-15.625 + t = 14.155939566

Solving
-15.625 + t = 14.155939566

Solving for variable 't'.

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

Add '15.625' to each side of the equation.
-15.625 + 15.625 + t = 14.155939566 + 15.625

Combine like terms: -15.625 + 15.625 = 0.000
0.000 + t = 14.155939566 + 15.625
t = 14.155939566 + 15.625

Combine like terms: 14.155939566 + 15.625 = 29.780939566
t = 29.780939566

Simplifying
t = 29.780939566


Subproblem 2
t + -15.625 = -14.155939566

Simplifying
t + -15.625 = -14.155939566

Reorder the terms:
-15.625 + t = -14.155939566

Solving
-15.625 + t = -14.155939566

Solving for variable 't'.

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

Add '15.625' to each side of the equation.
-15.625 + 15.625 + t = -14.155939566 + 15.625

Combine like terms: -15.625 + 15.625 = 0.000
0.000 + t = -14.155939566 + 15.625
t = -14.155939566 + 15.625

Combine like terms: -14.155939566 + 15.625 = 1.469060434
t = 1.469060434

Simplifying
t = 1.469060434


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {29.780939566, 1.469060434}
Solution
t = {29.780939566, 1.469060434}

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