Helping with homework!

[R515]

Please go easy on me as it's 35yrs since I did this at school! I'm helping my daughter and the equation is

x^2 - y^2 =12 where y = x-2 .

By substitution I've worked the answer out as x=4 but none of the methodology (e.g. factorisation or quadratic formula) in her notes or the text books give me the right answer. Through factorisation, x = -2 which is wrong, any one able to help as this driving me nuts!!

Rgds, Mark

[buddy]

the equation is

x^2 - y^2 =12 where y = x-2 .

What are you supposed to do with this? Are you solving a system of equations?

none of the methodology (e.g. factorisation or quadratic formula) in her notes or the text books give me the right answer.

Please show what you did so we can see what's going wrong.

Through factorisation, x = -2 which is wrong

How did you get this by factoring??

Substitution is what they show here for doing this.

x^2 - (x - 2)^2 = 12
x^2 - (x^2 - 4x + 4) = 12
etc

What did you get from this?

[R515]

Thanks for the reply, the question is to find the value of x and y, this is how it went using factorisation as my daughter has been taught:

x^2 - (x-2)^2 = 12
x^2 - (x-2)(x-2) = 12
x^2 -x^2 -4x +4 = 12
x^2 -x^2 -4x = 8
so -4x =8
which gives x= -2 but substituting -2 for x will not give the correct answer. Where are we going wrong?

Thx.

[buddy]

x^2 - (x-2)^2 = 12
x^2 - (x-2)(x-2) = 12
x^2 -x^2 -4x +4 = 12

Try doing grouping like I showed so you don't forget the minus:

x^2 - (x^2 - 4x + 4) = 12
x^2 - x^2 + 4x - 4 = 12

when you do the signs right the rest should come out right too.

[R515]

Thanks for taking the time to help, think I've nearly got it, is it the effect of removing the bracket on

x^2 -(x^2 +4x -4) =12

that turns +4x into -4x and -4 into +4 then as this is what makes it work out right with x=4 ?

Thanks Mark

[buddy]

is it the effect of removing the bracket on

x^2 -(x^2 +4x -4) =12

that turns +4x into -4x and -4 into +4 then as this is what makes it work out right with x=4 ?

Yeah it's the negatives. You can learn about doing negatives with brackets here. It's kind of important.

[R515]

Thanks for the help, it finally came to me yesterday evening how the (-) outside the bracket would influence what happens to the numbers inside when the brackets are removed, appreciate the help given,

Mark