Question 111116
#1



{{{x^2 +7x+10=0}}}


{{{(x+5)(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+5=0}}} or {{{x+2=0}}}


{{{x=-5}}} or {{{x=-2}}}  Now solve for x in each case



So our solutions are {{{x=-5}}} or {{{x=-2}}}



Notice if we graph {{{y=x^2 +7x+10}}} we get


{{{ graph(500,500,-10,10,-10,10, x^2 +7x+10) }}}


and we can see that the graph has roots at {{{x=-5}}} and {{{x=-2}}}, so this verifies our answer.


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#2




{{{3x^2-6x=0}}}


{{{x(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=0}}} or {{{x-2=0}}}


{{{x=0}}} or {{{x=2}}}  Now solve for x in each case



So our solutions are {{{x=0}}} or {{{x=2}}} 



Notice if we graph {{{y=3x^2-6x}}} we get


{{{ graph(500,500,-10,10,-10,10, 3x^2-6x) }}}


and we can see that the graph has roots at {{{x=0}}} and {{{x=2}}} , so this verifies our answer.