What is the solution to (x-7)^2=(x+3)^2?

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Homework Help Overview

The problem involves solving the equation (x-7)^2=(x+3)^2, which falls under the subject area of algebra, specifically dealing with quadratic equations and their properties.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss different methods for solving the equation, including squaring both sides and expanding the expressions. There is a question about the validity of inferring equality from the square roots of both sides.

Discussion Status

The discussion is ongoing with various approaches being explored. Some participants have offered guidance on alternative methods, such as expanding the squares instead of squaring both sides directly. There is a recognition of the need to clarify the implications of squaring in the context of the equation.

Contextual Notes

There is mention of a potential solution indicated in a textbook, which raises questions about the assumptions made in the original poster's approach. The discussion reflects on the implications of the mathematical principles involved.

mistalopez
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Homework Statement



(x-7)^2=(x+3)^2

2. The attempt at a solution

I squared both sides and received x-7=x+3

However, that cannot be correct because the variables cancel out which means there is no solution. The book shows that there is a solution of 2
 
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hi, instead of squaring both sides, try multiplying them out as you know (x-7)^2 is the same as (x-7)(x-7) ..
 
mistalopez said:
I squared both sides
You mean you took the square root of both sides?

Well, there's a problem: the phrase
a2 is the square of b​
is not synonymous with
a is b​

So you cannot infer that the two square roots are equal...
 
Supplementing what Hurkyl said, if a2 = b2, then a = +/b. You can apply this principle to your equation.
 

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