60=350t+500t^2

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Solution for 60=350t+500t^2 equation: 


Simplifying
60 = 350t + 500t2

Solving
60 = 350t + 500t2

Solving for variable 't'.

Reorder the terms:
60 + -350t + -500t2 = 350t + -350t + 500t2 + -500t2

Combine like terms: 350t + -350t = 0
60 + -350t + -500t2 = 0 + 500t2 + -500t2
60 + -350t + -500t2 = 500t2 + -500t2

Combine like terms: 500t2 + -500t2 = 0
60 + -350t + -500t2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(6 + -35t + -50t2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(6 + -35t + -50t2)' equal to zero and attempt to solve:

Simplifying
6 + -35t + -50t2 = 0

Solving
6 + -35t + -50t2 = 0

Begin completing the square.  Divide all terms by
-50 the coefficient of the squared term: 

Divide each side by '-50'.
-0.12 + 0.7t + t2 = 0.0

Move the constant term to the right:

Add '0.12' to each side of the equation.
-0.12 + 0.7t + 0.12 + t2 = 0.0 + 0.12

Reorder the terms:
-0.12 + 0.12 + 0.7t + t2 = 0.0 + 0.12

Combine like terms: -0.12 + 0.12 = 0.00
0.00 + 0.7t + t2 = 0.0 + 0.12
0.7t + t2 = 0.0 + 0.12

Combine like terms: 0.0 + 0.12 = 0.12
0.7t + t2 = 0.12

The t term is 0.7t.  Take half its coefficient (0.35).
Square it (0.1225) and add it to both sides.

Add '0.1225' to each side of the equation.
0.7t + 0.1225 + t2 = 0.12 + 0.1225

Reorder the terms:
0.1225 + 0.7t + t2 = 0.12 + 0.1225

Combine like terms: 0.12 + 0.1225 = 0.2425
0.1225 + 0.7t + t2 = 0.2425

Factor a perfect square on the left side:
(t + 0.35)(t + 0.35) = 0.2425

Calculate the square root of the right side: 0.49244289

Break this problem into two subproblems by setting 
(t + 0.35) equal to 0.49244289 and -0.49244289.


Subproblem 1
t + 0.35 = 0.49244289

Simplifying
t + 0.35 = 0.49244289

Reorder the terms:
0.35 + t = 0.49244289

Solving
0.35 + t = 0.49244289

Solving for variable 't'.

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

Add '-0.35' to each side of the equation.
0.35 + -0.35 + t = 0.49244289 + -0.35

Combine like terms: 0.35 + -0.35 = 0.00
0.00 + t = 0.49244289 + -0.35
t = 0.49244289 + -0.35

Combine like terms: 0.49244289 + -0.35 = 0.14244289
t = 0.14244289

Simplifying
t = 0.14244289


Subproblem 2
t + 0.35 = -0.49244289

Simplifying
t + 0.35 = -0.49244289

Reorder the terms:
0.35 + t = -0.49244289

Solving
0.35 + t = -0.49244289

Solving for variable 't'.

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

Add '-0.35' to each side of the equation.
0.35 + -0.35 + t = -0.49244289 + -0.35

Combine like terms: 0.35 + -0.35 = 0.00
0.00 + t = -0.49244289 + -0.35
t = -0.49244289 + -0.35

Combine like terms: -0.49244289 + -0.35 = -0.84244289
t = -0.84244289

Simplifying
t = -0.84244289


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.14244289, -0.84244289}
Solution
t = {0.14244289, -0.84244289}

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