Question 147606
{{{x*sqrt(2)+4=sqrt(3)}}} Start with the given equation.



{{{x*sqrt(2)=sqrt(3)-4}}} Subtract 4 from both sides.



{{{x=(sqrt(3)-4)/sqrt(2)}}} Divide both sides by {{{sqrt(2)}}} to isolate x.



{{{x=((sqrt(3)-4)/sqrt(2))(sqrt(2)/sqrt(2))}}}  Multiply both the numerator and denominator by {{{sqrt(2)}}}



{{{x=((sqrt(3)-4)sqrt(2))/(sqrt(2)sqrt(2))}}} Combine the fractions.



{{{x=((sqrt(3)-4)sqrt(2))/(2)}}} Multiply {{{sqrt(2)sqrt(2)}}} to get {{{sqrt(2)sqrt(2)=sqrt(2*2)=sqrt(2^2)=2}}}



{{{x=(sqrt(3)sqrt(2)-4*sqrt(2))/(2)}}} Distribute




{{{x=(sqrt(6)-4*sqrt(2))/(2)}}} Combine and multiply the square roots.



So our answer is {{{x=(sqrt(6)-4*sqrt(2))/(2)}}}