Question 980897

1.) 

{{{a^2+2(a+3)=0}}}


{{{a^2+2a+6=0}}}

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} ...note your coefficient {{{a=1}}}, unknown variable {{{x}}} is {{{a}}},  coefficient {{{ba=2}}}, and constant {{{c=6}}}


{{{a = (-2 +- sqrt( 2^2-4*1*6 ))/(2*1) }}}


{{{a = (-2 +- sqrt( 4-24 ))/2 }}}


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

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

{{{a = (-2 +- 2sqrt( 5 )*i)/2 }}}

{{{a = (-cross(2)1 +- cross(2)sqrt( 5 )*i)/cross(2) }}}

{{{a = (-1 +-sqrt( 5 )*i) }}}

solutions: there is no real solutions (so, there is no x-intercepts), just complex solutions


{{{a = -1 +sqrt( 5 )*i }}}

or

{{{a = -1 -sqrt( 5 )*i }}}






2.) 

{{{x^2-3(2x+3)=0}}}
{{{x^2-6x-9=0}}}

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

{{{x = (-(-6) +- sqrt( (-6)^2-4*1*(-9) ))/(2*1) }}}

{{{x = (6 +- sqrt( 36+36 ))/2 }}}

{{{x = (6 +- sqrt( 2*36 ))/2 }}}

{{{x = (6 +- sqrt( 2*6^2 ))/2 }}}

{{{x = (6 +- 6sqrt( 2 ))/2 }}}

{{{x = (cross(6)3 +- cross(6)3sqrt( 2 ))/cross(2)1 }}}

{{{x = (3 +- 3sqrt( 2 )) }}}

solutions:
exact
{{{x = 3 + 3sqrt( 2 ) }}}

or

{{{x = 3 -3sqrt( 2 ) }}}


approximate:

{{{x = 7.24 }}}

or

{{{x = -1.24 }}}


3.) 

{{{3y(y-5)=6}}}

{{{3y^2-15y=6}}}

{{{3y^2-15y-6=0}}}

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

{{{y = (-(-15) +- sqrt( (-15)^2-4*3*(-6) ))/(2*3) }}}

{{{y = (15 +- sqrt( 225+72 ))/6 }}}

{{{y = (15 +- sqrt( 297 ))/6 }}}

{{{y = (15 +- 17.23)/6 }}}

solutions:


{{{y = (15 + 17.23)/6 }}}

{{{y = 32.23/6 }}}

{{{y = 5.37 }}}

or

{{{y = (15 - 17.23)/6 }}}

{{{y = -2.23/6 }}}

{{{y = -0.37 }}}


4.) 

{{{2(3x^2+1) =0}}}

{{{6x^2+2 =0}}}

{{{6x^2 =-2}}}

{{{x^2 =-2/6}}}

{{{x^2 =-1/3}}}

{{{x =sqrt(-1/3)}}}

solutions: complex

{{{x =  sqrt(-1/3) }}}=>{{{x = sqrt(-1)/sqrt(3)}}}=>{{{x = i/sqrt(3)}}}


or

{{{x = - sqrt(-1/3) }}}=>{{{x = -sqrt(-1)/sqrt(3)}}}=>{{{x = -i/sqrt(3)}}}