Question 120418
a)





{{{x^2-6x-16=0}}} Start with the given equation


{{{(x-8)(x+2)=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:

{{{x-8=0}}} or  {{{x+2=0}}} 


{{{x=8}}} or  {{{x=-2}}}    Now solve for x in each case



So our answer is 

 {{{x=8}}} or  {{{x=-2}}} 



Notice if we graph {{{y=x^2-6x-16}}}  we can see that the roots are {{{x=8}}} and  {{{x=-2}}} . So this visually verifies our answer.



{{{ graph(500,500,-10,10,-10,10,0, x^2-6x-16) }}}



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b)




{{{6x^2+42x=0}}} Start with the given equation


{{{6x(x+7)=0}}} Factor the left side 




Now set each factor equal to zero:

{{{6x=0}}} or  {{{x+7=0}}} 


{{{x=0}}} or  {{{x=-7}}}    Now solve for x in each case



So our answer is 

 {{{x=0}}} or  {{{x=-7}}} 



Notice if we graph {{{y=6x^2+42x}}}  we can see that the roots are {{{x=0}}} and  {{{x=-7}}} . So this visually verifies our answer.



{{{ graph(500,500,-10,10,-10,10,0, 6x^2+42x) }}}