Question

The product of two consecutive odd integers is 99. Find the integers.

Short answer

The integers are 9 and 11.

Step-by-step solution

Given information 

The product of two consecutive odd integers is 99.

Solve the equation 

Let $n=$the first odd integer

$n+2=$the next odd integer.

The product of two consecutive odd integers is 99.

The product of the first odd integer and the second odd integer is 99.

$$\begin{gathered} \left(n\right)\left(n+2\right)=99 \\ {n}^2+2n=99 \\ {n}^2+2n-99=0 \\ a=1,b=2andc=-99 \\ \mathrm{Using}\mathrm{quadratic}\mathrm{formula} \\ \mathrm{n}=\frac{-\mathrm{b}\pm \sqrt{{\mathrm{b}}^2-4\mathrm{ac}}}{2\mathrm{a}} \end{gathered}$$

Substitution

Substitute the value of $a,b,$and$c$