-q^2=-8q-3

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Solution for -q^2=-8q-3 equation:


Simplifying
-1q2 = -8q + -3

Reorder the terms:
-1q2 = -3 + -8q

Solving
-1q2 = -3 + -8q

Solving for variable 'q'.

Reorder the terms:
3 + 8q + -1q2 = -3 + -8q + 3 + 8q

Reorder the terms:
3 + 8q + -1q2 = -3 + 3 + -8q + 8q

Combine like terms: -3 + 3 = 0
3 + 8q + -1q2 = 0 + -8q + 8q
3 + 8q + -1q2 = -8q + 8q

Combine like terms: -8q + 8q = 0
3 + 8q + -1q2 = 0

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

Divide each side by '-1'.
-3 + -8q + q2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -8q + 3 + q2 = 0 + 3

Reorder the terms:
-3 + 3 + -8q + q2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -8q + q2 = 0 + 3
-8q + q2 = 0 + 3

Combine like terms: 0 + 3 = 3
-8q + q2 = 3

The q term is -8q.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8q + 16 + q2 = 3 + 16

Reorder the terms:
16 + -8q + q2 = 3 + 16

Combine like terms: 3 + 16 = 19
16 + -8q + q2 = 19

Factor a perfect square on the left side:
(q + -4)(q + -4) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(q + -4) equal to 4.358898944 and -4.358898944.

Subproblem 1

q + -4 = 4.358898944 Simplifying q + -4 = 4.358898944 Reorder the terms: -4 + q = 4.358898944 Solving -4 + q = 4.358898944 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + q = 4.358898944 + 4 Combine like terms: -4 + 4 = 0 0 + q = 4.358898944 + 4 q = 4.358898944 + 4 Combine like terms: 4.358898944 + 4 = 8.358898944 q = 8.358898944 Simplifying q = 8.358898944

Subproblem 2

q + -4 = -4.358898944 Simplifying q + -4 = -4.358898944 Reorder the terms: -4 + q = -4.358898944 Solving -4 + q = -4.358898944 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + q = -4.358898944 + 4 Combine like terms: -4 + 4 = 0 0 + q = -4.358898944 + 4 q = -4.358898944 + 4 Combine like terms: -4.358898944 + 4 = -0.358898944 q = -0.358898944 Simplifying q = -0.358898944

Solution

The solution to the problem is based on the solutions from the subproblems. q = {8.358898944, -0.358898944}

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