Question 113950
{{{x(x - 10) + 9 = 0}}} Start with the given equation



{{{x^2 - 10x + 9 = 0}}} Distribute



{{{(x-9)(x-1)=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-9=0}}} or {{{x-1=0}}}


{{{x=9}}} or {{{x=1}}}  Now solve for x in each case



So our solutions are {{{x=9}}} or {{{x=1}}}



Notice if we graph {{{y=x^2-10x+9}}} we get


{{{ graph(500,500,-10,10,-10,10, x^2-10x+9) }}}


and we can see that the graph has roots at {{{x=9}}} and {{{x=1}}}, so this verifies our answer.