\((x+a)(x+b+ci)(x+b-ci)\)

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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