Question 132911
# 1




{{{9x^2-24x+16=0}}} Start with the given equation


{{{(3x-4)(3x-4)=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:

{{{3x-4=0}}} or  {{{3x-4=0}}} 


{{{x=4/3}}} or  {{{x=4/3}}}    Now solve for x in each case



Since we have a repeating answer, our only answer is {{{x=4/3}}}


Notice if we graph {{{y=9x^2-24x+16}}}  we can see that the only root is {{{x=4/3}}}. So this visually verifies our answer.



{{{ graph(500,500,-10,10,-10,10,0, 9x^2-24x+16) }}}




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# 2


{{{x^2-3x=40 }}}  Start with the given equation


{{{x^2-3x-40=0 }}}  Subtract 40 from both sides



{{{(x-8)(x+5)=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+5=0}}} 


{{{x=8}}} or  {{{x=-5}}}    Now solve for x in each case



So our answer is 

 {{{x=8}}} or  {{{x=-5}}} 



Notice if we graph {{{y=x^2-3x-40}}}  we can see that the roots are {{{x=8}}} and  {{{x=-5}}} . So this visually verifies our answer.



{{{ graph(500,500,-10,10,-10,10,0, x^2-3x-40) }}}