completing the square: Find 2 consec. pos. integers such tha

[jburgswife30]

Hey I need help with this one.

Find two consecutive positive integers such that the sum of their square is 85
here is what I have

x^2+(x+2)^2=85
x^2+x^2+4x+4=85
2x^2+4x+4=85
2x^2+4x=81
x^2+2x=40.5

I think I have messed up somewhere, (I know the problem is not done.)

 

[Mrspi]

Re: completing the square

Hey I need help with this one.

Find two consecutive positive integers such that the sum of their square is 85
here is what I have

x^2+(x+2)^2=85
x^2+x^2+4x+4=85
2x^2+4x+4=85
2x^2+4x=81
x^2+2x=40.5

I think I have messed up somewhere, (I know the problem is not done.)

You "messed up" in writing the original equation.

Let x = a positive integer
Then x + 1 = the next consecutive integer

x<SUP>2</SUP> + (x + 1)<SUP>2</SUP> = 85

See if that works out better for you.

 

[jburgswife30]

ok now I am getting this

x^2+(x+1)^2=85
x^2+x^2+x+2=85
2x^2+x+2=85
2x^2+4x=83
x^2+x=41.5

this can't be right either can it?

 

[o_O]

Try expanding (x + 1)² again. You made a bit of a mistake there. Use your FOIL (or whatever they call it) method:
(x + 1)(x + 1)

 

[jburgswife30]

i'm still not getting it but thanks

 

[galactus]

\(\displaystyle \L\\x^{2}+(x+1)^{2}=85\)

\(\displaystyle \L\\2x^{2}+2x-84=0\)

Factor:

\(\displaystyle \L\\2(x-6)(x+7)=0\)

x=6 or x=-7. It can't be -7 because it must be postive.

Your numbers are 6 and 7.

6^2+7^2=85