15.87=0.021T^2+0.296T+3.803

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Solution for 15.87=0.021T^2+0.296T+3.803 equation: 


Simplifying
15.87 = 0.021T2 + 0.296T + 3.803

Reorder the terms:
15.87 = 3.803 + 0.296T + 0.021T2

Solving
15.87 = 3.803 + 0.296T + 0.021T2

Solving for variable 'T'.

Combine like terms: 15.87 + -3.803 = 12.067
12.067 + -0.296T + -0.021T2 = 3.803 + 0.296T + 0.021T2 + -3.803 + -0.296T + -0.021T2

Reorder the terms:
12.067 + -0.296T + -0.021T2 = 3.803 + -3.803 + 0.296T + -0.296T + 0.021T2 + -0.021T2

Combine like terms: 3.803 + -3.803 = 0.000
12.067 + -0.296T + -0.021T2 = 0.000 + 0.296T + -0.296T + 0.021T2 + -0.021T2
12.067 + -0.296T + -0.021T2 = 0.296T + -0.296T + 0.021T2 + -0.021T2

Combine like terms: 0.296T + -0.296T = 0.000
12.067 + -0.296T + -0.021T2 = 0.000 + 0.021T2 + -0.021T2
12.067 + -0.296T + -0.021T2 = 0.021T2 + -0.021T2

Combine like terms: 0.021T2 + -0.021T2 = 0.000
12.067 + -0.296T + -0.021T2 = 0.000

Begin completing the square.  Divide all terms by
-0.021 the coefficient of the squared term: 

Divide each side by '-0.021'.
-574.6190476 + 14.0952381T + T2 = 0

Move the constant term to the right:

Add '574.6190476' to each side of the equation.
-574.6190476 + 14.0952381T + 574.6190476 + T2 = 0 + 574.6190476

Reorder the terms:
-574.6190476 + 574.6190476 + 14.0952381T + T2 = 0 + 574.6190476

Combine like terms: -574.6190476 + 574.6190476 = 0.0000000
0.0000000 + 14.0952381T + T2 = 0 + 574.6190476
14.0952381T + T2 = 0 + 574.6190476

Combine like terms: 0 + 574.6190476 = 574.6190476
14.0952381T + T2 = 574.6190476

The T term is 14.0952381T.  Take half its coefficient (7.04761905).
Square it (49.66893427) and add it to both sides.

Add '49.66893427' to each side of the equation.
14.0952381T + 49.66893427 + T2 = 574.6190476 + 49.66893427

Reorder the terms:
49.66893427 + 14.0952381T + T2 = 574.6190476 + 49.66893427

Combine like terms: 574.6190476 + 49.66893427 = 624.28798187
49.66893427 + 14.0952381T + T2 = 624.28798187

Factor a perfect square on the left side:
(T + 7.04761905)(T + 7.04761905) = 624.28798187

Calculate the square root of the right side: 24.985755579

Break this problem into two subproblems by setting 
(T + 7.04761905) equal to 24.985755579 and -24.985755579.


Subproblem 1
T + 7.04761905 = 24.985755579

Simplifying
T + 7.04761905 = 24.985755579

Reorder the terms:
7.04761905 + T = 24.985755579

Solving
7.04761905 + T = 24.985755579

Solving for variable 'T'.

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

Add '-7.04761905' to each side of the equation.
7.04761905 + -7.04761905 + T = 24.985755579 + -7.04761905

Combine like terms: 7.04761905 + -7.04761905 = 0.00000000
0.00000000 + T = 24.985755579 + -7.04761905
T = 24.985755579 + -7.04761905

Combine like terms: 24.985755579 + -7.04761905 = 17.938136529
T = 17.938136529

Simplifying
T = 17.938136529


Subproblem 2
T + 7.04761905 = -24.985755579

Simplifying
T + 7.04761905 = -24.985755579

Reorder the terms:
7.04761905 + T = -24.985755579

Solving
7.04761905 + T = -24.985755579

Solving for variable 'T'.

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

Add '-7.04761905' to each side of the equation.
7.04761905 + -7.04761905 + T = -24.985755579 + -7.04761905

Combine like terms: 7.04761905 + -7.04761905 = 0.00000000
0.00000000 + T = -24.985755579 + -7.04761905
T = -24.985755579 + -7.04761905

Combine like terms: -24.985755579 + -7.04761905 = -32.033374629
T = -32.033374629

Simplifying
T = -32.033374629


Solution
The solution to the problem is based on the solutions
from the subproblems.
T = {17.938136529, -32.033374629}

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