Question 684660


{{{x^2-14x-6=0}}} Start with the given equation.



Notice that the quadratic {{{x^2-14x-6}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=1}}}, {{{B=-14}}}, and {{{C=-6}}}



Let's use the quadratic formula to solve for "x":



{{{x = (-B +- sqrt( B^2-4AC ))/(2A)}}} Start with the quadratic formula



{{{x = (-(-14) +- sqrt( (-14)^2-4(1)(-6) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=-14}}}, and {{{C=-6}}}



{{{x = (14 +- sqrt( (-14)^2-4(1)(-6) ))/(2(1))}}} Negate {{{-14}}} to get {{{14}}}. 



{{{x = (14 +- sqrt( 196-4(1)(-6) ))/(2(1))}}} Square {{{-14}}} to get {{{196}}}. 



{{{x = (14 +- sqrt( 196--24 ))/(2(1))}}} Multiply {{{4(1)(-6)}}} to get {{{-24}}}



{{{x = (14 +- sqrt( 196+24 ))/(2(1))}}} Rewrite {{{sqrt(196--24)}}} as {{{sqrt(196+24)}}}



{{{x = (14 +- sqrt( 220 ))/(2(1))}}} Add {{{196}}} to {{{24}}} to get {{{220}}}



{{{x = (14 +- sqrt( 220 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (14 +- 2*sqrt(55))/(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 = (14)/(2) +- (2*sqrt(55))/(2)}}} Break up the fraction.  



{{{x = 7 +- sqrt(55)}}} Reduce.  



{{{x = 7+sqrt(55)}}} or {{{x = 7-sqrt(55)}}} Break up the expression.  



So the two exact solutions are {{{x = 7+sqrt(55)}}} or {{{x = 7-sqrt(55)}}}