Answer:
q = 16
Explanation:
x^2 + q = 8x
Rearrange:
x^2 -8x + q = 0
We are told the equation has equal roots. Lets assign the letter z to that root.
Since the equation has equal roots, it can be factored: (x + z)*(x + z)
x^2 -8x + q = (x+z)(x+z)
x^2 -8x + q = (x^2 +2zx + z^2)
Therefore:
1) -8x = 2zx, and
2) q = z^2
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Solve the first for z:
1) -8x = 2zx,
-8 = 2z
z = -4
Since q = z^2,
q = (-4)^2 or 16
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CHECK:
Does x^2 + 16 = 8x have equal roots?
x^2 + 16 = 8x
x^2 - 8x + 16 = 0
(x - 4)(x - 4) YES