Solve for q.q − 2 = –18q − 20 + 17q

Sure, let's solve the equation step by step.

The given equation is: q.q − 2 = –18q − 20 + 17q

Step 1: Simplify the right side of the equation. Combine like terms:

q.q - 2 = -18q + 17q - 20 q.q - 2 = -q - 20

Step 2: Rewrite the equation to bring all terms to one side:

q.q + q + 20 - 2 = 0 q.q + q + 18 = 0

Step 3: This is a quadratic equation in the form of ax^2 + bx + c = 0, where a = 1, b = 1, and c = 18.

Step 4: Solve for q using the quadratic formula, q = [-b ± sqrt(b^2 - 4ac)] / 2a:

q = [-1 ± sqrt((1)^2 - 4118)] / 2*1 q = [-1 ± sqrt(1 - 72)] / 2 q = [-1 ± sqrt(-71)] / 2

Since the square root of a negative number is not a real number, there are no real solutions for q in this equation. The solutions are complex numbers.