Maths query- Guide 3

[mneeti]

In Guide 3, chapter 3- Question no. 14 on page no. 49 :

x^2-10x+25 = 16

I tried solving the question as:

(x-5) (x-5) = 16

which gives only one answer:

x = 16+5
x = 21

However, the guide provides the answer as :

x^2-10x+9 = 0

x= 9, x=1

I agree with the above solution as provide in the guide, but I am not able to understand why my solution is not correct.

Please reply to the above.

Thanks !

[mengnu.liang]

You need to move all numbers to one side of the equation first before solving the problem.

1) X^2-10x+25-16=0 = I believe you forgot to subtract 16 from both side of the equation first.

[mneeti]

I understand that the equation is equated to "0" before solving. But all I want to understand is - if I solve the equation by equating it to 16; should not make any difference, this is just another way of solving the equation and should ideally be correct. Ain't it?

[mengnu.liang]

(x-5) (x-5) = 16

which gives only one answer:

x = 16+5
x = 21

Well, if you plug in 21 into (x-5) = 21-5 = 16*16 doesn't equal to 16.

[mneeti]

Oh yeah, that's correct.
A learning here-always check the solution. Thanks !

[tim]

when (x-5)(x-5) = 16, what you have is two of the same number multiplying to be 16. that number of course could be 4 or -4, so we have:

x-5 = 4

x-5 = -4

this will generate the two solutions you're looking for..