Question 151432


{{{x^2-3=0}}} Start with the given equation.



Take note that {{{x^2-3=0}}} really looks like {{{x^2+0x+(-3)=0}}}



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=1}}}, {{{b=0}}}, and {{{c=-3}}}



Let's use the quadratic formula to solve for x



{{{x = (-b +- sqrt( b^2-4ac ))/(2a)}}} Start with the quadratic formula



{{{x = (-(0) +- sqrt( (0)^2-4(1)(-3) ))/(2(1))}}} Plug in  {{{a=1}}}, {{{b=0}}}, and {{{c=-3}}}



{{{x = (-0 +- sqrt( 0-4(1)(-3) ))/(2(1))}}} Square {{{0}}} to get {{{0}}}. 



{{{x = (-0 +- sqrt( 0--12 ))/(2(1))}}} Multiply {{{4(1)(-3)}}} to get {{{-12}}}



{{{x = (-0 +- sqrt( 0+12 ))/(2(1))}}} Rewrite {{{sqrt(0--12)}}} as {{{sqrt(0+12)}}}



{{{x = (-0 +- sqrt( 12 ))/(2(1))}}} Add {{{0}}} to {{{12}}} to get {{{12}}}



{{{x = (-0 +- sqrt( 12 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (-0 +- 2*sqrt(3))/(2)}}} Simplify the square root  (note: If you need help with simplifying square roots, check out this <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  



{{{x = (-0)/(2) +- (2*sqrt(3))/(2)}}} Break up the fraction.  



{{{x = 0 +- sqrt(3)}}} Reduce.  



{{{x = sqrt(3)}}} or {{{x = -sqrt(3)}}} Break up the expression.  



So our answers are {{{x = sqrt(3)}}} or {{{x = -sqrt(3)}}} 



which approximate to {{{x=1.732}}} or {{{x=-1.732}}} 



Note: even though the quadratic formula works perfectly here, there is a much faster way to solve this problem.