Question 955338

1.

{{{x^2=-4x+21}}}

{{{x^2+4x-21=0}}}

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} ...since {{{a=1}}},{{{b=4}}}, and {{{c=-21}}}, we have

{{{x = (-4 +- sqrt( 4^2-4*1*(-21) ))/(2*1) }}}

{{{x = (-4 +- sqrt( 16+84 ))/2 }}}

{{{x = (-4 +- sqrt( 100 ))/2 }}}

{{{x = (-4 +- 10)/2 }}}

solutions:

{{{x = (-4 + 10)/2 }}}

{{{x =6/2 }}}

{{{x = 3}}}

and

{{{x = (-4 - 10)/2 }}}

{{{x = -14/2 }}}

{{{x = -7 }}}



2.

{{{x^2+5x+1=0}}}

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} ...since {{{a=1}}},{{{b=5}}}, and {{{c=1}}}, we have

{{{x = (-5 +- sqrt( 5^2-4*1*1 ))/(2*1) }}}

{{{x = (-5 +- sqrt( 25-4 ))/2 }}}

{{{x = (-5 +- sqrt( 21 ))/2 }}}

exact solutions:

{{{x = (-5 + sqrt( 21 ))/2 }}}
or
{{{x = (-5 - sqrt( 21 ))/2 }}}

approximate solutions:

{{{x = -0.2 }}}
or
{{{x = -4.8 }}}