The problem involves expressing the quadratic expression x^2 - 10x in the form (x+p)^2 + q. Participants are tasked with identifying the values of p and q.
The discussion includes various attempts to complete the square and clarify the relationship between the terms. Some participants express uncertainty about their calculations, while others provide insights into the process of finding p and q. There is no explicit consensus on the values, but multiple interpretations and methods are being explored.
Participants note the distinction between working with an expression versus an equation, and there are discussions about the implications of manipulating terms in the context of completing the square.
Haroldingo said:Homework Statement
Express x^2 - 10x in the form (x+p)^2 + q
State the value of P and Q
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?
Haroldingo said: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?
You're not working with an equation - just an expression.Haroldingo said:Ok so I complete the square because I'm more comfortable with that:
x^2 - 10x + 0 = 0
Didn't notice earlier, but this isn't correct.Haroldingo said:x^2 - 10x = 0
x^2 - 5^2 = 5^2
Starting at the beginning, you haveHaroldingo said:(x-5)^2 - 25
this would mean p = 5 and q = -25?
Haroldingo said:This doesn't seem right? Have I gone wrong somewhere?
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, <=>.Gliese123 said: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