Question

Identify the most appropriate method to use to solve each quadratic equation.

$$\begin{gathered} a)x^2+6x+8=0 \\ b){(n-3)}^2=16c)5p^2-6p=9 \end{gathered}$$

Short answer

The appropriate method is

a) We recognize that the left side of the equation is trinomial that can be easily factorized, so factoring will be the most appropriate method.

b) Quadratic formula will be an appropriate method.

c) Quadratic formula will be an appropriate method.

Step-by-step solution

Part a) step 1: Given information

We are given a quadratic equation$x^2+6x+8=0$

Identifying the appropriate solution

We recognize that the left side of the equation is trinomial that can be easily factorized, so factoring will be the most appropriate method.

Part b) Step 1: Given information 

We are given a quadratic equation${(n-3)}^2=16$

Part b) Step 2: simplifying and identifying the type of solution

On simplifying we get

$$\begin{gathered} n^2-6n+9=16 \\ {n}^2-6n-7=0 \end{gathered}$$

The Quadratic Formula is the most appropriate method.

Part c) Step 1: Given information

We are given a quadratic information$5p^2-6p=9$

Part c) Step 2: We simplify and find the appropriate solution

On simplifying we get,

$5p^2-6p-9=0$

For the above equation the Quadratic Formula is the most appropriate method.

Conclusion

The appropriate method is

a) We recognize that the left side of the equation is trinomial that can be easily factorized, so factoring will be the most appropriate method.

b) Quadratic formula will be an appropriate method

c) Quadratic formula will be an appropriate method