Express x^2 - 10x in the form (x+p)^2 + q

[Haroldingo]

1. The problem statement, all variables and given/known data

Express x^2 - 10x in the form (x+p)^2 + q

State the value of P and Q

3. The attempt at a solution

I don't know! I don't get it because when I times out the brackets p will always be a number, and there are no numbers that aren't multiplied by x in x squared minus 10 x. Gragh?

[Curious3141]

Expand this out: (x+p)^2 + q

Compare the coefficients of this expression to x^2 - 10x (the constant term here is zero, i.e. the expression can be written x^2 - 10x + 0). What equations can you set up to define p and q?

[eumyang]

Another way is to complete the square (http://www.mathsisfun.com/algebra/completing-square.html).

[Haroldingo]

Ok so I complete the square because i'm more comfortable with that:

x^2 - 10x + 0 = 0

x^2 - 10x = 0

x^2 - 5^2 = 5^2

(x-5)^2 - 25

this would mean p = 5 and q = -25?

This doesn't seem right? Have I gone wrong somewhere?

[Gliese123]

1. The problem statement, all variables and given/known data

Express x^2 - 10x in the form (x+p)^2 + q

State the value of P and Q

3. The attempt at a solution

I don't know! I don't get it because when I times out the brackets p will always be a number, and there are no numbers that aren't multiplied by x in x squared minus 10 x. Gragh?

Ok so I complete the square because i'm more comfortable with that:

x^2 - 10x + 0 = 0

x^2 - 10x = 0

x^2 - 5^2 = 5^2

(x-5)^2 - 25

this would mean p = 5 and q = -25?

This doesn't seem right? Have I gone wrong somewhere?

It should be right as you wrote:
x2-10x <=> (x+p)(x+p) + q <=> x2+2xp+p2+q.
x2-5x-5x+25-25 <=> x2-10x

p=5, q=-25

[evosy1978]

p=-5 q=-25

I find it quicker to half the x term.... so theres your p straight away -5

and then sqaure p so -5^2 = 25 and you need +0 so its -25...

another example is
x^2 - 6x + 30

so again half -6 is p= -3
then again square -3 = 9
and i need 30 so 9+21 q =21

[Haroldingo]

Cheers all, got the marks! :)

[Mark44]

Some quibbles:
Ok so I complete the square because i'm more comfortable with that:
x^2 - 10x + 0 = 0
You're not working with an equation - just an expression.


x^2 - 10x = 0

x^2 - 5^2 = 5^2
Didn't notice earlier, but this isn't correct.
Where did the -10x term go? And how is it that you can add -5^2 to one side of an equation, but add +5^2 to the other. The answer is, you can't do this.


(x-5)^2 - 25

this would mean p = 5 and q = -25?
Starting at the beginning, you have
x2 - 10x
= x2 - 10x + 25 - 25
= (x - 5)2 - 25
= (x + (-5))2 + (-25)
I leave it for you to figure out what p and q are.


This doesn't seem right? Have I gone wrong somewhere?

It should be right as you wrote:
x2-10x <=> (x+p)(x+p) + q <=> x2+2xp+p2+q.
x2-5x-5x+25-25 <=> x2-10x

p=5, q=-25
Gliese123, Do not connect expressions with an equivalent sign. Expressions that are equal should be connected with =. Statements such as equations or inequalities can in some cases be connected with the equivalent symbol, <=>.