Question 142538
{{{(x-2)^2 + x^2=10}}} Start with the given equation



{{{x^2-4x+4 + x^2=10}}} Foil



{{{x^2-4x+4 + x^2-10=0}}} Subtract 10 from both sides



{{{2x^2-4x-6=0}}} Combine like terms. This is where you made an error: {{{x^2}}} plus {{{x^2}}} is not {{{x^4}}}




{{{2(x-3)(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-3=0}}} or  {{{x+1=0}}} 


{{{x=3}}} or  {{{x=-1}}}    Now solve for x in each case



So our answer is 

 {{{x=3}}} or  {{{x=-1}}} 



Notice if we graph {{{y=2x^2-4x-6}}}  we can see that the roots are {{{x=3}}} and  {{{x=-1}}} . So this visually verifies our answer.



{{{ graph(500,500,-10,10,-10,10,0, 2x^2-4x-6) }}}