Q. 427 - Intermediate Algebra

Question

Solve Quadratic Equations by Factoring in following exercises, solve.

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

Step-by-Step Solution

Answer

The solutions of the given expression are $x=-4 and -5$. 

Step 1. Given and explanation

We have $x^2+9x+20$.

We will first simplify the equation by factorizing.

We will then every factor equal to zero according to the zero product property to find the values.

Step 2. Simplifying the equation by factorizing.

We have $x^2+9x+20$.

We can write this as $x^2+4x+5x+20$.

Simplifying it,

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

Step 3. Finding values.

We now have $(x+4)(x+5)=0$.

Putting each factor equal to zero gives us,

1. $$\begin{gathered} x+4=0 \\ x=-4 \end{gathered}$$
   
2. $$\begin{gathered} x+5=0 \\ x=-5 \end{gathered}$$
   

This shows that values are $-4 and -5$.

Step 4. Check the solution.

We will check the solution by putting the value of the solution in the equation separately. If the equation satisfies, our answer is right.  

1. When $x=-4$
   $$\begin{gathered} {(-4)}^2+9(-4)+20=0 \\ 16-36+20=0 \\ 36-36=0 \\ 0=0 \end{gathered}$$
   Hence satisfied.
2. When $x=-5$
   $$\begin{gathered} {(-5)}^2+9(-5)+20=0 \\ 25-45+20=0 \\ 45-45=0 \\ 0=0 \end{gathered}$$
   Hence satisfied.

Thus our calculations are right.