Chapter 5 - Section 5.8 - Solving Equations by Factoring and Problem Solving - Exercise Set: 47

$x=\{ -7,4 \}$

Work Step by Step

The factored form of the given expression, $(x-1)(x+4)=24$, is \begin{array}{} x^2+4x-x-4=24 \\\\ x^2+3x-4-24=0 \\\\ x^2+3x-28=0 \\\\ (x+7)(x-4)=0 .\end{array} Equating each factor to zero, then \begin{array}{l} x+7=0 \\ x=0-7 \\ x=-7 ,\text{ OR}\\\\ x-4=0 \\ x=0+4 \\ x=4 \end{array} Hence, $x=\{ -7,4 \}$.

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