SOLUTION: can you help me solve by using the quadratic formula. x^2=x+8

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Question 80999: can you help me solve by using the quadratic formula.
x^2=x+8
Answer by praseenakos@yahoo.com(507) About Me  (Show Source):
You can put this solution on YOUR website!
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+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+


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+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+



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


==> x+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A1%2A%28-8%29+%29%29%2F%282%2A1%29+



==> x+=+%281+%2B-+sqrt%28+1+%2B+32+%29%29%2F2+


==> x+=+%281+%2B-+sqrt%28+1+%2B+32+%29%29%2F2+



==> x+=+%281+%2B-+sqrt%28+33%29%29%2F2+



==> 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