PLZZZZZZZZ HELP gcse?

Question

X^2+6X=(X+h)^2+K

FIND THE VALUES OF K AND OF X.

Answer 1

The best I can do would be just to transpose to find K and X ie.

X^2+6X=(X+h)^2+K remove brackets
X^2+6X=X^2+h^2+K move elements to other side
X^2+6X-X^2=h^2+K move elements to other side
X^2+6X-X^2-h^2 =K move around
X^2-X^2+6X-h^2 = K tidy up
6X-h^2 = K

Same to find X

X^2+6X=(X+h)^2+K remove brackets
X^2+6X=X^2+h^2+K move elements to other side
6X=X^2+h^2+K-x^2 tidy up
6X=h^2+K move 6 to other side
X=(h^2+K)/6

Answer 2

Yes, this can be solved by using the method of completing the square. Hope you have studied this.

Generally x^2 + bx = (x + b/2)^2 - (b/2)^2

So, taking the LHS we have:

x^2 + 6x = (x + 6/2)^2 - (6/2)^2

x^2 + 6x = (x + 3)^2 - 9

Now compare the RHS with your original expression, we have:

(x +3)^2 - 9 = (x + h)^2 + K

Hence h = 3 and K = -9

Hope this helps.

Answer 3

x^2 + 6X = X^2 + 2hX + h^2 + K

by comparing coefficients:=
In 'X^2' is one (1)
In 'x'
6 = 2h
h = 3
In number
zero'0' = h^2 + K
but h = 3 therefor
0 = 3^2 + K
0 =9 + K
K = -9

NB I think you mean the values of 'h' and 'K'.

Answer 4

You cannot find out the values of 2 unknowns with one equation only. You need to have atleast 2 equations.

Answer 5

you haven't given the value of h?