Algebra
posted by John .
I got a couple I want to check my work :
Both are Solve using the quadratic formula :
1) x^23x=7x2
x^23x7x+2=7x7x2+2
x^210x+2=0
x = 10 + sqrt10^2  4(1)(2) / 2(1)
x = 10 + sqrt100  8 / 2
x = 10 + sqrt92 / 2
x = 10 + 2sqrt23 /2
x = 5 + sqrt23
x = 5 + sqrt23 and x = 5  sqrt23
2) x^27x1= 7
x^27x+71 = 7+7
x^27x+6 = 0
x = 7 + sqrt7^2  4(1)(6) / 2(1)
x = 7 + sqrt4924 / 2
x = 7 + sqrt25 / 2
x = 7 + 5 / 2
x = 7+5 / 2 , x = 12 / 2 , x = 6
x = 75 / 2 , x = 2 / 2 , x = 1

The second one looks ok. I think step 7 of problem 1 has an error.

Ok so what I did was
x = 10 + 2sqrt23 / 2
I divided 10 by 2 and 2 by 2
Thats how i got
x = 5 + sqrt23 
1) x^23x=7x2
x^23x7x+2=7x7x2+2
x^210x+2=0
x = 10 + sqrt10^2  4(1)(2) / 2(1)
x = 10 + sqrt100  8 / 2
x = 10 + sqrt92 / 2 OK to here. See below.
x = 10 + 2sqrt23 /2
x = 5 + sqrt23
x = 5 + sqrt23 and x = 5  sqrt23
x = (10+sqrt 92)/2
x = (10+sqrt 2(46)/2
(What you are doing here is dividing 10 by 2, which is correct, as well as 2/2, which also is correct. What is NOT correct is dividing 46 by 2 (you are using the divisor of 2 twice but the divisor of 2 disappeared when you used it to divide the 10 and 2 of 2*46).
x = (5+sqrt 46) 
7x2=22.5