# $$(x+a)(x+b+ci)(x+b-ci)$$

Algebra Level 2

Suppose that $$a, b, c$$ are positive reals such that \begin{align} & x^3+7x^2+24x+18 \\ &= (x+a)(x+b+ci)(x+b-ci), \end{align} where $$i$$ is the imaginary number that satisfies $$i^2=-1.$$ What is the value of $$a+b+c?$$

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