Question
Solve 16x2−64=0using the difference of squares pattern.(1 point)Responsesx=−2x is equal to negative 2x=−2and x=2x is equal to negative 2 and x is equal to 2x=2x is equal to 2x=−8and x=8
Answers
Answered by
GPT-4o mini
To solve the equation \(16x^2 - 64 = 0\) using the difference of squares pattern, we can first rewrite the equation in a suitable form.
1. Start with the original equation:
\[
16x^2 - 64 = 0
\]
2. We can factor out a common factor, which in this case is 16:
\[
16(x^2 - 4) = 0
\]
3. Next, we can set the expression inside the parenthesis equal to zero:
\[
x^2 - 4 = 0
\]
4. Now we recognize that this is a difference of squares, which can be factored further:
\[
(x - 2)(x + 2) = 0
\]
5. Setting each factor equal to zero gives us the solutions:
\[
x - 2 = 0 \quad \Rightarrow \quad x = 2
\]
\[
x + 2 = 0 \quad \Rightarrow \quad x = -2
\]
Thus, the solutions are:
\[
x = -2 \quad \text{and} \quad x = 2
\]
So the correct response is:
**x is equal to negative 2 and x is equal to 2.**
1. Start with the original equation:
\[
16x^2 - 64 = 0
\]
2. We can factor out a common factor, which in this case is 16:
\[
16(x^2 - 4) = 0
\]
3. Next, we can set the expression inside the parenthesis equal to zero:
\[
x^2 - 4 = 0
\]
4. Now we recognize that this is a difference of squares, which can be factored further:
\[
(x - 2)(x + 2) = 0
\]
5. Setting each factor equal to zero gives us the solutions:
\[
x - 2 = 0 \quad \Rightarrow \quad x = 2
\]
\[
x + 2 = 0 \quad \Rightarrow \quad x = -2
\]
Thus, the solutions are:
\[
x = -2 \quad \text{and} \quad x = 2
\]
So the correct response is:
**x is equal to negative 2 and x is equal to 2.**