50=82.144177+-0.829392Q+0.0021324Q^2

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Solution for 50=82.144177+-0.829392Q+0.0021324Q^2 equation:


Simplifying
50 = 82.144177 + -0.829392Q + 0.0021324Q2

Solving
50 = 82.144177 + -0.829392Q + 0.0021324Q2

Solving for variable 'Q'.

Combine like terms: 50 + -82.144177 = -32.144177
-32.144177 + 0.829392Q + -0.0021324Q2 = 82.144177 + -0.829392Q + 0.0021324Q2 + -82.144177 + 0.829392Q + -0.0021324Q2

Reorder the terms:
-32.144177 + 0.829392Q + -0.0021324Q2 = 82.144177 + -82.144177 + -0.829392Q + 0.829392Q + 0.0021324Q2 + -0.0021324Q2

Combine like terms: 82.144177 + -82.144177 = 0.000000
-32.144177 + 0.829392Q + -0.0021324Q2 = 0.000000 + -0.829392Q + 0.829392Q + 0.0021324Q2 + -0.0021324Q2
-32.144177 + 0.829392Q + -0.0021324Q2 = -0.829392Q + 0.829392Q + 0.0021324Q2 + -0.0021324Q2

Combine like terms: -0.829392Q + 0.829392Q = 0.000000
-32.144177 + 0.829392Q + -0.0021324Q2 = 0.000000 + 0.0021324Q2 + -0.0021324Q2
-32.144177 + 0.829392Q + -0.0021324Q2 = 0.0021324Q2 + -0.0021324Q2

Combine like terms: 0.0021324Q2 + -0.0021324Q2 = 0.0000000
-32.144177 + 0.829392Q + -0.0021324Q2 = 0.0000000

Begin completing the square.  Divide all terms by
-0.0021324 the coefficient of the squared term: 

Divide each side by '-0.0021324'.
15074.17792 + -388.9476646Q + Q2 = 0

Move the constant term to the right:

Add '-15074.17792' to each side of the equation.
15074.17792 + -388.9476646Q + -15074.17792 + Q2 = 0 + -15074.17792

Reorder the terms:
15074.17792 + -15074.17792 + -388.9476646Q + Q2 = 0 + -15074.17792

Combine like terms: 15074.17792 + -15074.17792 = 0.00000
0.00000 + -388.9476646Q + Q2 = 0 + -15074.17792
-388.9476646Q + Q2 = 0 + -15074.17792

Combine like terms: 0 + -15074.17792 = -15074.17792
-388.9476646Q + Q2 = -15074.17792

The Q term is -388.9476646Q.  Take half its coefficient (-194.4738323).
Square it (37820.07145) and add it to both sides.

Add '37820.07145' to each side of the equation.
-388.9476646Q + 37820.07145 + Q2 = -15074.17792 + 37820.07145

Reorder the terms:
37820.07145 + -388.9476646Q + Q2 = -15074.17792 + 37820.07145

Combine like terms: -15074.17792 + 37820.07145 = 22745.89353
37820.07145 + -388.9476646Q + Q2 = 22745.89353

Factor a perfect square on the left side:
(Q + -194.4738323)(Q + -194.4738323) = 22745.89353

Calculate the square root of the right side: 150.81741786

Break this problem into two subproblems by setting 
(Q + -194.4738323) equal to 150.81741786 and -150.81741786.

Subproblem 1

Q + -194.4738323 = 150.81741786 Simplifying Q + -194.4738323 = 150.81741786 Reorder the terms: -194.4738323 + Q = 150.81741786 Solving -194.4738323 + Q = 150.81741786 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '194.4738323' to each side of the equation. -194.4738323 + 194.4738323 + Q = 150.81741786 + 194.4738323 Combine like terms: -194.4738323 + 194.4738323 = 0.0000000 0.0000000 + Q = 150.81741786 + 194.4738323 Q = 150.81741786 + 194.4738323 Combine like terms: 150.81741786 + 194.4738323 = 345.29125016 Q = 345.29125016 Simplifying Q = 345.29125016

Subproblem 2

Q + -194.4738323 = -150.81741786 Simplifying Q + -194.4738323 = -150.81741786 Reorder the terms: -194.4738323 + Q = -150.81741786 Solving -194.4738323 + Q = -150.81741786 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '194.4738323' to each side of the equation. -194.4738323 + 194.4738323 + Q = -150.81741786 + 194.4738323 Combine like terms: -194.4738323 + 194.4738323 = 0.0000000 0.0000000 + Q = -150.81741786 + 194.4738323 Q = -150.81741786 + 194.4738323 Combine like terms: -150.81741786 + 194.4738323 = 43.65641444 Q = 43.65641444 Simplifying Q = 43.65641444

Solution

The solution to the problem is based on the solutions from the subproblems. Q = {345.29125016, 43.65641444}

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