-16t^2+100t+140=0

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Solution for -16t^2+100t+140=0 equation: 


Simplifying
-16t2 + 100t + 140 = 0

Reorder the terms:
140 + 100t + -16t2 = 0

Solving
140 + 100t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(35 + 25t + -4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(35 + 25t + -4t2)' equal to zero and attempt to solve:

Simplifying
35 + 25t + -4t2 = 0

Solving
35 + 25t + -4t2 = 0

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

Divide each side by '-4'.
-8.75 + -6.25t + t2 = 0

Move the constant term to the right:

Add '8.75' to each side of the equation.
-8.75 + -6.25t + 8.75 + t2 = 0 + 8.75

Reorder the terms:
-8.75 + 8.75 + -6.25t + t2 = 0 + 8.75

Combine like terms: -8.75 + 8.75 = 0.00
0.00 + -6.25t + t2 = 0 + 8.75
-6.25t + t2 = 0 + 8.75

Combine like terms: 0 + 8.75 = 8.75
-6.25t + t2 = 8.75

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 = 8.75 + 9.765625

Reorder the terms:
9.765625 + -6.25t + t2 = 8.75 + 9.765625

Combine like terms: 8.75 + 9.765625 = 18.515625
9.765625 + -6.25t + t2 = 18.515625

Factor a perfect square on the left side:
(t + -3.125)(t + -3.125) = 18.515625

Calculate the square root of the right side: 4.30297862

Break this problem into two subproblems by setting 
(t + -3.125) equal to 4.30297862 and -4.30297862.


Subproblem 1
t + -3.125 = 4.30297862

Simplifying
t + -3.125 = 4.30297862

Reorder the terms:
-3.125 + t = 4.30297862

Solving
-3.125 + t = 4.30297862

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 = 4.30297862 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + t = 4.30297862 + 3.125
t = 4.30297862 + 3.125

Combine like terms: 4.30297862 + 3.125 = 7.42797862
t = 7.42797862

Simplifying
t = 7.42797862


Subproblem 2
t + -3.125 = -4.30297862

Simplifying
t + -3.125 = -4.30297862

Reorder the terms:
-3.125 + t = -4.30297862

Solving
-3.125 + t = -4.30297862

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 = -4.30297862 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + t = -4.30297862 + 3.125
t = -4.30297862 + 3.125

Combine like terms: -4.30297862 + 3.125 = -1.17797862
t = -1.17797862

Simplifying
t = -1.17797862


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.42797862, -1.17797862}
Solution
t = {7.42797862, -1.17797862}

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