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OK, this looks like a quadratic equation, which means a polynomial whose highest power is two:
-3r^2 + 21r + 24 = 0
The general form for a quadratic equation is
ax^2 + bx + c = 0
and the general solution is given by the quadratic formula:
x = [ -b +- sqrt(b^2 - 4ac) ] / 2a
Because a quadratic equation is second order, it has two solutions, or roots. The +- symbol means to use the "+" sign first, and then use the "-" sign. It is read as "plus or minus."
So, if we replace the x with your r, and the coefficients, a, b, c, with the ones from your equation, we get for a solution:
r = [-21 +- sqrt(21^2 - 4 * -3 * 24) ] / 2 * -3
When you do the arithmetic using the "+" sign, you get -1 for the first root, and using the "-" sign you get 8 for the second root.
So, the solutions are -1 and 8, which you can verify by plugging either of these into the original equation.
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What is radius of hemisphere whose total surface area is 942 cm?
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