Question

Solve:

$b^2+9b+14=0$

Short answer

The solutions of the quadratic equations $b^2+9b+14=0$are $b=-7,-2$

Step-by-step solution

Step 1. Given Information

An equation:

$b^2+9b+14=0$

Step 2. Factor the quadratic expression

Factorize the equation,

$$\begin{gathered} b^2+9b+14=0 \\ (b+2)(b+7)=0 \end{gathered}$$

Step 3. Use the Zero-Product property

Use the Zero Product Property and set each factor to zero.

$$\begin{gathered} b+2=0 \\ b=-2 \\ b+7=0 \\ b=-7 \end{gathered}$$

The value of b is $b=-2,-7$

Step 4. Check the answer

Check by substituting the values in the original equation,

When $b=-2$,

$$\begin{gathered} {(-2)}^2+9(-2)+14=0 \\ 4-18+14=0 \\ 18-18=0 \end{gathered}$$

When $b=-7$,

$$\begin{gathered} {(-7)}^2+9(-7)+14=0 \\ 49-63+14=0 \\ 63-63=0 \end{gathered}$$

Hence the equations hold true.