Question 144978

{{{4x^2-16=0}}} Start with the given equation



{{{4(x^2-4)=0}}} Factor out the GCF 4



{{{4(x+2)(x-2)=0}}} Factor the left side using the difference of squares formula {{{A^2-B^2=(A+B)(A-B)}}}



Now set each factor equal to zero:


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


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



So our answers are
 

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



Notice if we graph {{{y=4x^2-16}}}  we can see that the roots are {{{x=-2}}} and  {{{x=2}}} . So this visually verifies our answer.



{{{ graph(500,500,-10,10,-10,10,0, 4x^2-16) }}}