Question 145774

{{{x^2+7x+10=0}}} Start with the given equation.



{{{(x+5)*(x+2)=0}}} Factor the left side. If you need me to go in depth about factoring, please let me know.



{{{x+5=0}}} or {{{x+2=0}}}  Set each factor equal to zero. Remember, if {{{A*B=0}}} then either {{{A=0}}} or {{{B=0}}}.



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 Let's solve the 1st equation {{{x+5=0}}}



{{{x+5=0}}} Start with the given equation.



{{{x=-5}}} Subtract {{{5}}} from both sides.



 So our 1st answer is {{{x=-5}}}.



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 Now let's solve the 2nd equation {{{x+2=0}}}



{{{x+2=0}}} Start with the given equation.



{{{x=-2}}} Subtract {{{2}}} from both sides.



 So our 2nd answer is {{{x=-2}}}.



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Answer:



So our answers are:



{{{x=-5}}} or {{{x=-2}}}



 Notice that when we graph {{{y=x^2+7x+10}}}, we can see that the graph crosses the x-axis at {{{x=-5}}} and {{{x=-2}}}. So this visually verifies our answer.


 {{{graph(500,500,-10,10,-10,10,x^2+7x+10)}}} Graph of {{{y=x^2+7x+10}}}