Question 626473
{{{x^2-2x-13=0}}} Start with the given equation.



Notice that the quadratic {{{x^2-2x-13}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=1}}}, {{{B=-2}}}, and {{{C=-13}}}



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



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



{{{x = (-(-2) +- sqrt( (-2)^2-4(1)(-13) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=-2}}}, and {{{C=-13}}}



{{{x = (2 +- sqrt( (-2)^2-4(1)(-13) ))/(2(1))}}} Negate {{{-2}}} to get {{{2}}}. 



{{{x = (2 +- sqrt( 4-4(1)(-13) ))/(2(1))}}} Square {{{-2}}} to get {{{4}}}. 



{{{x = (2 +- sqrt( 4--52 ))/(2(1))}}} Multiply {{{4(1)(-13)}}} to get {{{-52}}}



{{{x = (2 +- sqrt( 4+52 ))/(2(1))}}} Rewrite {{{sqrt(4--52)}}} as {{{sqrt(4+52)}}}



{{{x = (2 +- sqrt( 56 ))/(2(1))}}} Add {{{4}}} to {{{52}}} to get {{{56}}}



{{{x = (2 +- sqrt( 56 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



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



{{{x = 1 +- sqrt(14)}}} Reduce.  



{{{x = 1+sqrt(14)}}} or {{{x = 1-sqrt(14)}}} Break up the expression.  



So the solutions are {{{x = 1+sqrt(14)}}} or {{{x = 1-sqrt(14)}}} 


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