Question 758657


(a) 
{{{x^2 + 6x + 7 = 0}}}

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

{{{x = (-6 +- sqrt( 6^2-4*1*7 ))/(2*1) }}}


{{{x = (-6 +- sqrt(36-28 ))/2}}}

{{{x = (-6 +- sqrt(8 ))/2}}}

{{{x = (-6 +- 2.8284)/2}}}

solutions:

{{{x = (-6 + 2.8284)/2}}}

{{{x = (-3.1716)/2}}}

{{{x = -1.5858}}}

or

{{{x = (-6 - 2.8284)/2}}}

{{{x = (-8.8284)/2}}}

{{{x = -4.4142}}}


(b) 

{{{3x^2 - x - 7 = 0}}}

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

{{{x = (-(-1) +- sqrt( (-1)^2-4*3*(-7) ))/(2*3) }}}


{{{x = (1 +- sqrt(1+84 ))/6}}}

{{{x = (1 +- sqrt(85 ))/6}}}

{{{x = (1 +- 9.2195)/6}}}

solutions:

{{{x = (1 + 9.2195)/6}}}

{{{x = 10.2195/6}}}

{{{x =1.7033}}}

or

{{{x = (1 - 9.2195)/6}}}

{{{x = (-8.2195)/6}}}

{{{x = -1.3699}}}


(c) 

{{{x^2 - 3x - 3.51 = 0}}}

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

{{{x = (-(-3) +- sqrt((-3)^2-4*1*(-3.51) ))/(2*1) }}}

{{{x = (3 +- sqrt(9+14.04 ))/2 }}}

{{{x = (3 +- sqrt(23.04 ))/2 }}}

{{{x = (3 +- 4.8)/2 }}}

solutions:

{{{x = (3 + 4.8)/2 }}}

{{{x = 7.8/2 }}}

{{{x = 3.9 }}}...to four decimal places {{{x = 3.9000 }}}

or

{{{x = (3 - 4.8)/2 }}}

{{{x = -1.8/2 }}}

{{{x = -0.9 }}}..to four decimal places {{{x = -0.9000 }}}