SOLUTION: Can you help me double check this using the quad formula?: x^2 - 10 - 1 = -10

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Can you help me double check this using the quad formula?: x^2 - 10 - 1 = -10      Log On


   

Question 86539: Can you help me double check this using the quad formula?:
x^2 - 10 - 1 = -10
Answer by praseenakos@yahoo.com(507) About Me  (Show Source):
You can put this solution on YOUR website!

Hope your question is like this ...


+x%5E2+-+10x+-+1+=+-10+


Answer:
Factorisation method

+x%5E2+-+10x+-+1+=+-10+

Add 10 to both sides of the equation....


+x%5E2+-+10x+-+1+%2B+10++=+-10+%2B+10+


==> +x%5E2+-+10x++%2B+9+=+0+


You can split the middle term as follows...
Here remember that you have to find out two numbers whose sum is -10(that is coefficient of x and whose product is +9(that is the constant term....

+x%5E2+-+9x+-1x++%2B+9+=+0+


==> +%28x%5E2+-+9x%29+-+1%281x++-+9%29+=+0+


==> +x%28x+-+9%29+-+1%28x+-+9%29+=+0+



Here (x-9) is common to both the terms....so you can take it outside...


==> (x - 9 ) ( x- 1) = 0


==> either (x-9) =0 or (x-1) = 0


==> x = 9 or x = 1


So the solution is x = 9 or x = 1


Using Quadratic formula...

+x%5E2+-+10x+-+1+=+-10+

Question can be written as
+x%5E2+-+10x++%2B+9+=+0+


then the solution is given by,


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

where a = 1, b= -10 and c = +9


==> x+=+%28-%28-10%29+%2B-+sqrt%28+%28-10%29%5E2-4%2A1%2A9+%29%29%2F%282%2A1%29+



==> x+=+%2810+%2B-+sqrt%28+100+-36+%29%29%2F%282%29+


==> x+=+%2810+%2B-+sqrt%28+64+%29%29%2F%282%29+




==> x+=+%2810+%2B-++8+%29%2F%282%29+


==> x+=+%2810+%2B+8+%29%2F%282%29+ or x+=+%2810+-++8+%29%2F%282%29+


==> x+=+%2818+%29%2F%282%29+ or x+=+%282%29%2F%282%29+



==> x+=+9+ or x+=+1+

So the solution is x = 9 or x = 1



Hope you found the explanation useful......


Regards...

Praseena.