-9q=q^2-2

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Solution for -9q=q^2-2 equation:


Simplifying
-9q = q2 + -2

Reorder the terms:
-9q = -2 + q2

Solving
-9q = -2 + q2

Solving for variable 'q'.

Reorder the terms:
2 + -9q + -1q2 = -2 + q2 + 2 + -1q2

Reorder the terms:
2 + -9q + -1q2 = -2 + 2 + q2 + -1q2

Combine like terms: -2 + 2 = 0
2 + -9q + -1q2 = 0 + q2 + -1q2
2 + -9q + -1q2 = q2 + -1q2

Combine like terms: q2 + -1q2 = 0
2 + -9q + -1q2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-2 + 9q + q2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 9q + 2 + q2 = 0 + 2

Reorder the terms:
-2 + 2 + 9q + q2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 9q + q2 = 0 + 2
9q + q2 = 0 + 2

Combine like terms: 0 + 2 = 2
9q + q2 = 2

The q term is 9q.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9q + 20.25 + q2 = 2 + 20.25

Reorder the terms:
20.25 + 9q + q2 = 2 + 20.25

Combine like terms: 2 + 20.25 = 22.25
20.25 + 9q + q2 = 22.25

Factor a perfect square on the left side:
(q + 4.5)(q + 4.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(q + 4.5) equal to 4.716990566 and -4.716990566.

Subproblem 1

q + 4.5 = 4.716990566 Simplifying q + 4.5 = 4.716990566 Reorder the terms: 4.5 + q = 4.716990566 Solving 4.5 + q = 4.716990566 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + q = 4.716990566 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + q = 4.716990566 + -4.5 q = 4.716990566 + -4.5 Combine like terms: 4.716990566 + -4.5 = 0.216990566 q = 0.216990566 Simplifying q = 0.216990566

Subproblem 2

q + 4.5 = -4.716990566 Simplifying q + 4.5 = -4.716990566 Reorder the terms: 4.5 + q = -4.716990566 Solving 4.5 + q = -4.716990566 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + q = -4.716990566 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + q = -4.716990566 + -4.5 q = -4.716990566 + -4.5 Combine like terms: -4.716990566 + -4.5 = -9.216990566 q = -9.216990566 Simplifying q = -9.216990566

Solution

The solution to the problem is based on the solutions from the subproblems. q = {0.216990566, -9.216990566}

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