Question 336283
{{{7x^2-2=0 }}} can be written as {{{7x^2+0x-2=0}}}. 



{{{7x^2+0x-2=0}}} Start with the given equation.



Notice that the quadratic {{{7x^2+0x-2}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=7}}}, {{{B=0}}}, and {{{C=-2}}}



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(7)(-2) ))/(2(7))}}} Plug in  {{{A=7}}}, {{{B=0}}}, and {{{C=-2}}}



{{{x = (0 +- sqrt( 0-4(7)(-2) ))/(2(7))}}} Square {{{0}}} to get {{{0}}}. 



{{{x = (0 +- sqrt( 0--56 ))/(2(7))}}} Multiply {{{4(7)(-2)}}} to get {{{-56}}}



{{{x = (0 +- sqrt( 0+56 ))/(2(7))}}} Rewrite {{{sqrt(0--56)}}} as {{{sqrt(0+56)}}}



{{{x = (0 +- sqrt( 56 ))/(2(7))}}} Add {{{0}}} to {{{56}}} to get {{{56}}}



{{{x = (0 +- sqrt( 56 ))/(14)}}} Multiply {{{2}}} and {{{7}}} to get {{{14}}}. 



{{{x = (0 +- 2*sqrt(14))/(14)}}} 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*sqrt(14))/(14)}}} or {{{x = (0-2*sqrt(14))/(14)}}} Break up the expression.  



{{{x = (sqrt(14))/(7)}}} or {{{x = -(sqrt(14))/(7)}}} Reduce and simplify.  



So the solutions are {{{x = (sqrt(14))/(7)}}} or {{{x = -(sqrt(14))/(7)}}}  



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Jim