Chapter 7 - Polynomial Equations and Factoring - 7.4 - Solving Polynomial Equations in Factored Form - Monitoring Progress - Page 380: 8

$a=0$ and $a=-5$.

The given equation is $\Rightarrow a^2+5a=0$ Factor out $a$. $\Rightarrow a(a+5)=0$ Use zero-product property rule. $\Rightarrow a=0$ or $a+5=0$ Solve for $a$. $\Rightarrow a=0$ or $a=-5$ Check:- $a=0$ $\Rightarrow 0(0+5)=0$ $\Rightarrow 0(5)=0$ $\Rightarrow 0=0$ True. Check:- $a=-5$ $\Rightarrow -5(-5+5)=0$ $\Rightarrow -5(0)=0$ $\Rightarrow 0=0$ True. Hence, the solutions are $a=0$ and $a=-5$.