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

[mistalopez]

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

 

[krhisjun]

hi, instead of squaring both sides, try multiplying them out as you know (x-7)^2 is the same as (x-7)(x-7) ..

 

[Hurkyl]

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...

 

[Mark44]

Supplementing what Hurkyl said, if a² = b², then a = +/b. You can apply this principle to your equation.