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To find the values of q and p, we need to use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

In this case, a = 2, b = q, and c = -(p+8).

Plugging these values into the quadratic formula, we get:

x = (-q ± √(q² - 4(2)(-(p+8)))) / 2(2) x = (-q ± √(q² + 8p + 32)) / 4

Since this equation has two solutions, we can set it equal to zero and solve for q and p:

(-q ± √(q² + 8p + 32)) / 4 = 0

Solving for q:

-q ± √(q² + 8p + 32) = 0 √(q² + 8p + 32) = q q² + 8p + 32 = q² 8p + 32 = 0 8p = -32 p = -4

Therefore, the value of p is -4.

Now, substituting p = -4 back into the equation:

-q ± √(q² + 8(-4) + 32) = 0 -q ± √(q² - 8) = 0 q = ±√(q² - 8)

Solving for q:

q = √(q² - 8) q² = q² - 8 0 = -8

Since this equation has no solution, there is no valid value for q.