Question

In the following exercises, solve:

$x^2+9x+20=0$.

Short answer

The solution for the equation is,

$$\begin{gathered} x=-4 \\ x=-5 \end{gathered}$$

Step-by-step solution

Step 1. Given Information.

The equation is,

$x^2+9x+20=0$.

Step 2. Finding the solution.

$x^2+9x+20=0$.

Splitting the middle term such that the sum of the terms is $9$and the product of the terms is $20$,

$$\begin{gathered} \Rightarrow x^2+4x+5x+20=0 \\ \Rightarrow (x^2+4x)+(5x+20)=0 \\ \Rightarrow x(x+4)+5(x+4)=0 \\ \Rightarrow (x+4)(x+5)=0 \\ \Rightarrow x+4=0 \end{gathered}$$

or, role="math" localid="1647719897934" $$\begin{gathered} x+5=0 \\ \Rightarrow x=-4 \end{gathered}$$

or,$x=-5$