Question 538092


{{{x^2-14x+74=0}}} Start with the given equation.



Notice that the quadratic {{{x^2-14x+74}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=1}}}, {{{B=-14}}}, and {{{C=74}}}



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)(74) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=-14}}}, and {{{C=74}}}



{{{x = (14 +- sqrt( (-14)^2-4(1)(74) ))/(2(1))}}} Negate {{{-14}}} to get {{{14}}}. 



{{{x = (14 +- sqrt( 196-4(1)(74) ))/(2(1))}}} Square {{{-14}}} to get {{{196}}}. 



{{{x = (14 +- sqrt( 196-296 ))/(2(1))}}} Multiply {{{4(1)(74)}}} to get {{{296}}}



{{{x = (14 +- sqrt( -100 ))/(2(1))}}} Subtract {{{296}}} from {{{196}}} to get {{{-100}}}



{{{x = (14 +- sqrt( -100 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (14 +- 10*i)/(2)}}} Take the square root of {{{-100}}} to get {{{10*i}}}. 



{{{x = (14 + 10*i)/(2)}}} or {{{x = (14 - 10*i)/(2)}}} Break up the expression. 



{{{x = (14)/(2) + (10*i)/(2)}}} or {{{x =  (14)/(2) - (10*i)/(2)}}} Break up the fraction for each case. 



{{{x = 7+5*i}}} or {{{x =  7-5*i}}} Reduce. 



{{{x = 7+5*i}}} or {{{x = 7-5*i}}} Simplify. 



So the solutions are {{{x = 7+5*i}}} or {{{x = 7-5*i}}} 



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