Question 80999
QUESTION:



solve by using the quadratic formula.

x^2=x+8



ANSWER:


A general quadratic equation is given by,



ax^2 + bx + c = 0 ------------------(1)



Using quadratic formula, its solution is given by,



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



The given equation is,


x^2=x+8


this can be written as follows....
(here we need to bring the terms from right hand side of the equation to left hand side of the equation.)


x^2 = x + 8


Subtract x from both sides of the equation...then we have



x^2 - x = x - x + 8



==> x^2 -x = 8



Subtract 8 from both sides


==>x^2 -x - 8  = 8 - 8 


==> x^2 -x - 8 = 0 ----------------(2)


This is in the form of a quadratic equation.




Now compare (1) and (2)


then we have,


a = 1  b = -1 and c = -8




Now solution is given by,


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




substitute the values of a, b and in c in this formula,



==> {{{x = (-(-1) +- sqrt( (-1)^2-4*1*(-8) ))/(2*1) }}}




==> {{{x = (1 +- sqrt( 1 + 32 ))/2 }}}



==> {{{x = (1 +- sqrt( 1 + 32 ))/2 }}}




==> {{{x = (1 +- sqrt( 33))/2 }}}




==> x = (1 + sqrt 33)/2  or (1 - sqrt 33)/2





You can further simplify by giving approximate value os sqrt of 33 which is 5.75




so x = ( 1 + 5.75)/2 or x = (1 -5.75)/2





==> x = 6.75/2  or  x = -4.75/2



==> x = 3.375 or x = -2.375




Hope you found the explanation useful.




Regards.



Praseena