Question 147535

{{{x = (-b +- sqrt( b^2-4ac ))/(2a)}}} Start with the quadratic formula



{{{x = (-(-3) +- sqrt( (-3)^2-4(2)(1) ))/(2(2))}}} Plug in  {{{a=2}}}, {{{b=-3}}}, and {{{c=1}}}



{{{x = (3 +- sqrt( (-3)^2-4(2)(1) ))/(2(2))}}} Negate {{{-3}}} to get {{{3}}}. 



{{{x = (3 +- sqrt( 9-4(2)(1) ))/(2(2))}}} Square {{{-3}}} to get {{{9}}}. 



{{{x = (3 +- sqrt( 9-8 ))/(2(2))}}} Multiply {{{4(2)(1)}}} to get {{{8}}}



{{{x = (3 +- sqrt( 1 ))/(2(2))}}} Subtract {{{8}}} from {{{9}}} to get {{{1}}}



{{{x = (3 +- sqrt( 1 ))/(4)}}} Multiply {{{2}}} and {{{2}}} to get {{{4}}}. 



{{{x = (3 +- 1)/(4)}}} Take the square root of {{{1}}} to get {{{1}}}. 



{{{x = (3 + 1)/(4)}}} or {{{x = (3 - 1)/(4)}}} Break up the expression. 



{{{x = (4)/(4)}}} or {{{x =  (2)/(4)}}} Combine like terms. 



{{{x = 1}}} or {{{x = 1/2}}} Simplify. 



So our answers are {{{x = 1}}} or {{{x = 1/2}}}