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

In summary, the conversation discusses the solution of the equation (x-7)^2=(x+3)^2, with one person attempting to solve it by squaring both sides and the other pointing out that taking the square root of both sides is necessary. They also discuss the difference between the phrases "a2 is the square of b" and "a is b" and how it applies to the equation.
  • #1
mistalopez
16
0

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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  • #2
hi, instead of squaring both sides, try multiplying them out as you know (x-7)^2 is the same as (x-7)(x-7) ..
 
  • #3
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...
 
  • #4
Supplementing what Hurkyl said, if a2 = b2, then a = +/b. You can apply this principle to your equation.
 

1. How do you extract a square root?

To extract a square root, you can use the long division method or the prime factorization method. The long division method involves dividing the number into equal parts until you reach a perfect square. The prime factorization method involves writing the number as a product of its prime factors and taking out the square roots of the perfect squares in the factorization.

2. Is extracting a square root the same as finding the square root?

Yes, extracting a square root and finding the square root are two terms that refer to the same process. It involves finding the number that, when multiplied by itself, gives the original number.

3. Can you extract a square root for any number?

No, not all numbers have a perfect square root. A perfect square root is a number whose square root is a whole number. For example, the square root of 9 is 3, which is a whole number. However, the square root of 7 is not a whole number and is considered an irrational number.

4. What is the symbol for extracting a square root?

The symbol for extracting a square root is √. This is called the radical symbol and is used to represent the square root of a number. For example, √9 represents the square root of 9, which is 3.

5. What are some real-life applications of extracting a square root?

Extracting a square root is used in many fields such as engineering, physics, and finance. In engineering, it is used to calculate the length of sides in a right triangle. In physics, it is used in equations involving acceleration and velocity. In finance, it is used to calculate compound interest or to find the standard deviation in statistical analysis.

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