250t^2+100t+550=3000

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Solution for 250t^2+100t+550=3000 equation: 


Simplifying
250t2 + 100t + 550 = 3000

Reorder the terms:
550 + 100t + 250t2 = 3000

Solving
550 + 100t + 250t2 = 3000

Solving for variable 't'.

Reorder the terms:
550 + -3000 + 100t + 250t2 = 3000 + -3000

Combine like terms: 550 + -3000 = -2450
-2450 + 100t + 250t2 = 3000 + -3000

Combine like terms: 3000 + -3000 = 0
-2450 + 100t + 250t2 = 0

Factor out the Greatest Common Factor (GCF), '50'.
50(-49 + 2t + 5t2) = 0

Ignore the factor 50.

Subproblem 1
Set the factor '(-49 + 2t + 5t2)' equal to zero and attempt to solve:

Simplifying
-49 + 2t + 5t2 = 0

Solving
-49 + 2t + 5t2 = 0

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

Divide each side by '5'.
-9.8 + 0.4t + t2 = 0

Move the constant term to the right:

Add '9.8' to each side of the equation.
-9.8 + 0.4t + 9.8 + t2 = 0 + 9.8

Reorder the terms:
-9.8 + 9.8 + 0.4t + t2 = 0 + 9.8

Combine like terms: -9.8 + 9.8 = 0.0
0.0 + 0.4t + t2 = 0 + 9.8
0.4t + t2 = 0 + 9.8

Combine like terms: 0 + 9.8 = 9.8
0.4t + t2 = 9.8

The t term is 0.4t.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4t + 0.04 + t2 = 9.8 + 0.04

Reorder the terms:
0.04 + 0.4t + t2 = 9.8 + 0.04

Combine like terms: 9.8 + 0.04 = 9.84
0.04 + 0.4t + t2 = 9.84

Factor a perfect square on the left side:
(t + 0.2)(t + 0.2) = 9.84

Calculate the square root of the right side: 3.136877428

Break this problem into two subproblems by setting 
(t + 0.2) equal to 3.136877428 and -3.136877428.


Subproblem 1
t + 0.2 = 3.136877428

Simplifying
t + 0.2 = 3.136877428

Reorder the terms:
0.2 + t = 3.136877428

Solving
0.2 + t = 3.136877428

Solving for variable 't'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + t = 3.136877428 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + t = 3.136877428 + -0.2
t = 3.136877428 + -0.2

Combine like terms: 3.136877428 + -0.2 = 2.936877428
t = 2.936877428

Simplifying
t = 2.936877428


Subproblem 2
t + 0.2 = -3.136877428

Simplifying
t + 0.2 = -3.136877428

Reorder the terms:
0.2 + t = -3.136877428

Solving
0.2 + t = -3.136877428

Solving for variable 't'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + t = -3.136877428 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + t = -3.136877428 + -0.2
t = -3.136877428 + -0.2

Combine like terms: -3.136877428 + -0.2 = -3.336877428
t = -3.336877428

Simplifying
t = -3.336877428


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.936877428, -3.336877428}
Solution
t = {2.936877428, -3.336877428}

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