Question 208120
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^2+3w=18}}} Start with the given equation.



{{{w^2+3w-18=0}}} Subtract 18 from both sides.



{{{(w+6)(w-3)=0}}} Factor the left side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:


{{{w+6=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^2+3w=18}}} Start with the given equation.



{{{w^2+3w-18=0}}} Subtract 18 from both sides.



Notice that the quadratic {{{w^2+3w-18}}} is in the form of {{{Aw^2+Bw+C}}} where {{{A=1}}}, {{{B=3}}}, and {{{C=-18}}}



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



{{{w = (-B +- sqrt( B^2-4AC ))/(2A)}}} Start with the quadratic formula



{{{w = (-(3) +- sqrt( (3)^2-4(1)(-18) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=3}}}, and {{{C=-18}}}



{{{w = (-3 +- sqrt( 9-4(1)(-18) ))/(2(1))}}} Square {{{3}}} to get {{{9}}}. 



{{{w = (-3 +- sqrt( 9--72 ))/(2(1))}}} Multiply {{{4(1)(-18)}}} to get {{{-72}}}



{{{w = (-3 +- sqrt( 9+72 ))/(2(1))}}} Rewrite {{{sqrt(9--72)}}} as {{{sqrt(9+72)}}}



{{{w = (-3 +- sqrt( 81 ))/(2(1))}}} Add {{{9}}} to {{{72}}} to get {{{81}}}



{{{w = (-3 +- sqrt( 81 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{w = (-3 +- 9)/(2)}}} Take the square root of {{{81}}} to get {{{9}}}. 



{{{w = (-3 + 9)/(2)}}} or {{{w = (-3 - 9)/(2)}}} Break up the expression. 



{{{w = (6)/(2)}}} or {{{w =  (-12)/(2)}}} 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.