-16t^2+140t+30=20

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Solution for -16t^2+140t+30=20 equation: 


Simplifying
-16t2 + 140t + 30 = 20

Reorder the terms:
30 + 140t + -16t2 = 20

Solving
30 + 140t + -16t2 = 20

Solving for variable 't'.

Reorder the terms:
30 + -20 + 140t + -16t2 = 20 + -20

Combine like terms: 30 + -20 = 10
10 + 140t + -16t2 = 20 + -20

Combine like terms: 20 + -20 = 0
10 + 140t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 70t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + 70t + -8t2)' equal to zero and attempt to solve:

Simplifying
5 + 70t + -8t2 = 0

Solving
5 + 70t + -8t2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-0.625 + -8.75t + t2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + -8.75t + 0.625 + t2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + -8.75t + t2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + -8.75t + t2 = 0 + 0.625
-8.75t + t2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
-8.75t + t2 = 0.625

The t term is -8.75t.  Take half its coefficient (-4.375).
Square it (19.140625) and add it to both sides.

Add '19.140625' to each side of the equation.
-8.75t + 19.140625 + t2 = 0.625 + 19.140625

Reorder the terms:
19.140625 + -8.75t + t2 = 0.625 + 19.140625

Combine like terms: 0.625 + 19.140625 = 19.765625
19.140625 + -8.75t + t2 = 19.765625

Factor a perfect square on the left side:
(t + -4.375)(t + -4.375) = 19.765625

Calculate the square root of the right side: 4.445854811

Break this problem into two subproblems by setting 
(t + -4.375) equal to 4.445854811 and -4.445854811.


Subproblem 1
t + -4.375 = 4.445854811

Simplifying
t + -4.375 = 4.445854811

Reorder the terms:
-4.375 + t = 4.445854811

Solving
-4.375 + t = 4.445854811

Solving for variable 't'.

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

Add '4.375' to each side of the equation.
-4.375 + 4.375 + t = 4.445854811 + 4.375

Combine like terms: -4.375 + 4.375 = 0.000
0.000 + t = 4.445854811 + 4.375
t = 4.445854811 + 4.375

Combine like terms: 4.445854811 + 4.375 = 8.820854811
t = 8.820854811

Simplifying
t = 8.820854811


Subproblem 2
t + -4.375 = -4.445854811

Simplifying
t + -4.375 = -4.445854811

Reorder the terms:
-4.375 + t = -4.445854811

Solving
-4.375 + t = -4.445854811

Solving for variable 't'.

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

Add '4.375' to each side of the equation.
-4.375 + 4.375 + t = -4.445854811 + 4.375

Combine like terms: -4.375 + 4.375 = 0.000
0.000 + t = -4.445854811 + 4.375
t = -4.445854811 + 4.375

Combine like terms: -4.445854811 + 4.375 = -0.070854811
t = -0.070854811

Simplifying
t = -0.070854811


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {8.820854811, -0.070854811}
Solution
t = {8.820854811, -0.070854811}

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