SOLUTION: I am trying to solve the following equations but I am having trouble. 1. (x+h)(x+k)=0. Do I use the FOIL method x^2+xk+hx+hk=0 2. w^2+3w=18. I am not sure where to start wit

Question 208120This question is from textbook Elementary and intermediate algebra
: I am trying to solve the following equations but I am having trouble.
1. (x+h)(x+k)=0. Do I use the FOIL method x^2+xk+hx+hk=0
2. w^2+3w=18. I am not sure where to start with this one.
w^2+3w-18
w^2+6w-3w-18
w(w+6)-3(w+6)
-3w(w+6)
I am totally lost for solving 'w'. Can you help me?
This question is from textbook Elementary and intermediate algebra

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
1.

You use the zero product property here. Simply set each factor equal to zero and solve for 'x' in each case.

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2.

There are two ways to do this

Method # 1 Factoring and the Zero Product Property

Start with the given equation.

Subtract 18 from both sides.

Factor the left side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:

or

or Now solve for w in each case

So the solutions are or

--------------------------------------------------------

Or...

Method # 2 The Quadratic Formula

Start with the given equation.

Subtract 18 from both sides.

Notice that the quadratic is in the form of where , , and

Let's use the quadratic formula to solve for "w":

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the solutions are or

Why am I showing you the quadratic formula when factoring clearly works here? It turns out that you cannot factor every quadratic. However, the quadratic formula can solve any quadratic.
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