```Question 78915
I interpret your problem to involve solving for c in the equation:
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{{{C = sqrt(3C - 8)}}}
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square both sides to get:
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{{{C^2 = 3C - 8}}}
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get this into the standard quadratic form by subtracting 3C - 8 from both sides so that the
right side becomes zero.  With this subtraction you get:
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{{{C^2 - 3C + 8 = 0}}}
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This does not factor nicely so use the quadratic formula to solve. In the quadratic
formula you know that for an equation of the form:
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{{{ax^2 + bx + c = 0}}}
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the values of x that satisfy this equation (or in other words, the answers) are:
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{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
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For your problem x = C, and by comparison with the standard form, a = 1, b = -3, and c = 8.
Substitute these values into the answer form and you get:
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{{{C = (-(-3) +- sqrt( (-3)^2-4*1*8 ))/(2*1) }}}
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which simplifies to:
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{{{C = (3 +- sqrt(9 -32))/(2)}}}
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and by working on the radical you get:
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{{{C = (3 +- sqrt(-23))/2}}}
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and by substituting {{{i^2 = -1}}} under the radical the two answers become:
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{{{C = (3+-i*sqrt(23))/2}}}
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Hope I interpreted the problem correctly and that this clarifies the problem for you.

```