Question 785528


{{{x^2-x-2=x+2}}}

{{{x^2-2x-4=0}}}

{{{(x+__)(x-__)}}}......since you have {{{-2x-4}}}, you can't complete the square like this {{{(x+__)(x-__)}}}

so, to find solutions, use quadratic formula:

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

{{{x = (-(-2) +- sqrt( (-2)^2-4*1*(-4) ))/(2*1) }}}

{{{x = (2 +- sqrt( 4+16 ))/2 }}}

{{{x = (2 +- sqrt( 20 ))/2 }}}

{{{x = (2 +- sqrt( 4*5 ))/2 }}}

{{{x = (2 +- 2sqrt( 5))/2 }}}....simplify

{{{x =1 +- sqrt( 5) }}}

solutions:

{{{x =1 +sqrt( 5) }}}  => {{{x =1 +2.24 }}} => {{{x=3.24}}}

{{{x =1-sqrt( 5) }}}  => {{{x =1 -2.24 }}} => {{{x=-1.24}}}


{{{ graph( 600, 600, -10, 10, -10, 10, x+2, x^2-x-2) }}}