Question 131639
{{{x(x-20)=-100}}} Start with the given equation



{{{x^2-20x=-100}}} Distribute



{{{x^2-20x+100=0}}}  Add 100 to both sides. 



{{{(x-10)(x-10)=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-10=0}}} or  {{{x-10=0}}} 


{{{x=10}}} or  {{{x=10}}}    Now solve for x in each case



Since we have a repeating answer, our only answer is {{{x=10}}}


Notice if we graph {{{y=x^2-20x+100}}}  we can see that the only root is {{{x=10}}}. So this visually verifies our answer.



{{{ graph(500,500,-5,15,-10,10,0, x^2-20x+100) }}}