Question 251828
Take note that {{{(sqrt(5))^2=sqrt(5)*sqrt(5)=sqrt(5*5)=sqrt(25)=5}}}. So {{{(sqrt(5))^2=5}}}. Also, keep in mind that {{{((1/2)x)^2=(1/4)x^2}}}



{{{((1/2)x)^2+(x)^2=(sqrt(5))^2}}} Start with the given equation.



{{{(1/4)x^2+x^2=5}}} Square the individual terms (see above).



{{{(5/4)x^2=5}}} Combine like terms (this just amounts to adding fractions).



{{{5x^2=5*4}}} Multiply both sides by 4.



{{{x^2=(5*4)/5}}} Divide both sides by 5.



{{{x^2=(cross(5)*4)/cross(5)}}} Cancel out the common terms.



{{{x^2=4}}} Simplify.



{{{x=""+-sqrt(4)}}} Take the square root of both sides.



{{{x=sqrt(4)}}} or {{{x=-sqrt(4)}}} Break up the "plus/minus" to form two equations.



{{{x=2}}} or {{{x=-2}}}  Take the square root of {{{4}}} to get {{{2}}}.



{{{x=2}}} or {{{x=-2}}} Combine like terms.



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Answer:



So the solutions are {{{x=2}}} or {{{x=-2}}}.