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

Algebra ->  Polynomials-and-rational-expressions -> 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      Log On


   

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) About Me  (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



w%5E2%2B3w=18 Start with the given equation.


w%5E2%2B3w-18=0 Subtract 18 from both sides.


%28w%2B6%29%28w-3%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:

w%2B6=0 or w-3=0

w=-6 or w=3 Now solve for w in each case


So the solutions are w=-6 or w=3



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Or...

Method # 2 The Quadratic Formula



w%5E2%2B3w=18 Start with the given equation.


w%5E2%2B3w-18=0 Subtract 18 from both sides.


Notice that the quadratic w%5E2%2B3w-18 is in the form of Aw%5E2%2BBw%2BC where A=1, B=3, and C=-18


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


w+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


w+=+%28-%283%29+%2B-+sqrt%28+%283%29%5E2-4%281%29%28-18%29+%29%29%2F%282%281%29%29 Plug in A=1, B=3, and C=-18


w+=+%28-3+%2B-+sqrt%28+9-4%281%29%28-18%29+%29%29%2F%282%281%29%29 Square 3 to get 9.


w+=+%28-3+%2B-+sqrt%28+9--72+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-18%29 to get -72


w+=+%28-3+%2B-+sqrt%28+9%2B72+%29%29%2F%282%281%29%29 Rewrite sqrt%289--72%29 as sqrt%289%2B72%29


w+=+%28-3+%2B-+sqrt%28+81+%29%29%2F%282%281%29%29 Add 9 to 72 to get 81


w+=+%28-3+%2B-+sqrt%28+81+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


w+=+%28-3+%2B-+9%29%2F%282%29 Take the square root of 81 to get 9.


w+=+%28-3+%2B+9%29%2F%282%29 or w+=+%28-3+-+9%29%2F%282%29 Break up the expression.


w+=+%286%29%2F%282%29 or w+=++%28-12%29%2F%282%29 Combine like terms.


w+=+3 or w+=+-6 Simplify.


So the solutions are w+=+3 or w+=+-6


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.