0.5Q-5=70-Q^2

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Solution for 0.5Q-5=70-Q^2 equation: 


Simplifying
0.5Q + -5 = 70 + -1Q2

Reorder the terms:
-5 + 0.5Q = 70 + -1Q2

Solving
-5 + 0.5Q = 70 + -1Q2

Solving for variable 'Q'.

Reorder the terms:
-5 + -70 + 0.5Q + Q2 = 70 + -1Q2 + -70 + Q2

Combine like terms: -5 + -70 = -75
-75 + 0.5Q + Q2 = 70 + -1Q2 + -70 + Q2

Reorder the terms:
-75 + 0.5Q + Q2 = 70 + -70 + -1Q2 + Q2

Combine like terms: 70 + -70 = 0
-75 + 0.5Q + Q2 = 0 + -1Q2 + Q2
-75 + 0.5Q + Q2 = -1Q2 + Q2

Combine like terms: -1Q2 + Q2 = 0
-75 + 0.5Q + Q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '75' to each side of the equation.
-75 + 0.5Q + 75 + Q2 = 0 + 75

Reorder the terms:
-75 + 75 + 0.5Q + Q2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + 0.5Q + Q2 = 0 + 75
0.5Q + Q2 = 0 + 75

Combine like terms: 0 + 75 = 75
0.5Q + Q2 = 75

The Q term is 0.5Q.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5Q + 0.0625 + Q2 = 75 + 0.0625

Reorder the terms:
0.0625 + 0.5Q + Q2 = 75 + 0.0625

Combine like terms: 75 + 0.0625 = 75.0625
0.0625 + 0.5Q + Q2 = 75.0625

Factor a perfect square on the left side:
(Q + 0.25)(Q + 0.25) = 75.0625

Calculate the square root of the right side: 8.663861726

Break this problem into two subproblems by setting 
(Q + 0.25) equal to 8.663861726 and -8.663861726.


Subproblem 1
Q + 0.25 = 8.663861726

Simplifying
Q + 0.25 = 8.663861726

Reorder the terms:
0.25 + Q = 8.663861726

Solving
0.25 + Q = 8.663861726

Solving for variable 'Q'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + Q = 8.663861726 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + Q = 8.663861726 + -0.25
Q = 8.663861726 + -0.25

Combine like terms: 8.663861726 + -0.25 = 8.413861726
Q = 8.413861726

Simplifying
Q = 8.413861726


Subproblem 2
Q + 0.25 = -8.663861726

Simplifying
Q + 0.25 = -8.663861726

Reorder the terms:
0.25 + Q = -8.663861726

Solving
0.25 + Q = -8.663861726

Solving for variable 'Q'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + Q = -8.663861726 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + Q = -8.663861726 + -0.25
Q = -8.663861726 + -0.25

Combine like terms: -8.663861726 + -0.25 = -8.913861726
Q = -8.913861726

Simplifying
Q = -8.913861726


Solution
The solution to the problem is based on the solutions
from the subproblems.
Q = {8.413861726, -8.913861726}

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