Question 299575


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



Notice that the quadratic {{{x^2-7x+7}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=1}}}, {{{B=-7}}}, and {{{C=7}}}



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



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



{{{x = (-(-7) +- sqrt( (-7)^2-4(1)(7) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=-7}}}, and {{{C=7}}}



{{{x = (7 +- sqrt( (-7)^2-4(1)(7) ))/(2(1))}}} Negate {{{-7}}} to get {{{7}}}. 



{{{x = (7 +- sqrt( 49-4(1)(7) ))/(2(1))}}} Square {{{-7}}} to get {{{49}}}. 



{{{x = (7 +- sqrt( 49-28 ))/(2(1))}}} Multiply {{{4(1)(7)}}} to get {{{28}}}



{{{x = (7 +- sqrt( 21 ))/(2(1))}}} Subtract {{{28}}} from {{{49}}} to get {{{21}}}



{{{x = (7 +- sqrt( 21 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (7+sqrt(21))/(2)}}} or {{{x = (7-sqrt(21))/(2)}}} Break up the expression.  



So the solutions are {{{x = (7+sqrt(21))/(2)}}} or {{{x = (7-sqrt(21))/(2)}}}