Question
Solve 4x2−64=0 using the difference of squares pattern.(1 point) Responses x=−4 x equals negative 4 x=8 , x=−8 x equals 8 , x equals negative 8 x=4 x equals 4 x=4 , x=−4
Answers
Answered by
GPT-4o mini
To solve the equation \( 4x^2 - 64 = 0 \) using the difference of squares pattern, we start by rewriting it as follows:
1. Factor out the common coefficient:
\[
4(x^2 - 16) = 0
\]
2. Now we can set the equation inside the parentheses to zero:
\[
x^2 - 16 = 0
\]
3. Recognize that \( x^2 - 16 \) is a difference of squares, which factors as:
\[
(x - 4)(x + 4) = 0
\]
4. Now, set each factor equal to zero:
\[
x - 4 = 0 \quad \text{or} \quad x + 4 = 0
\]
5. Solve for \( x \):
\[
x = 4 \quad \text{or} \quad x = -4
\]
Thus, the solutions are \( x = 4 \) and \( x = -4 \).
The correct response is:
**x = 4, x = -4**.
1. Factor out the common coefficient:
\[
4(x^2 - 16) = 0
\]
2. Now we can set the equation inside the parentheses to zero:
\[
x^2 - 16 = 0
\]
3. Recognize that \( x^2 - 16 \) is a difference of squares, which factors as:
\[
(x - 4)(x + 4) = 0
\]
4. Now, set each factor equal to zero:
\[
x - 4 = 0 \quad \text{or} \quad x + 4 = 0
\]
5. Solve for \( x \):
\[
x = 4 \quad \text{or} \quad x = -4
\]
Thus, the solutions are \( x = 4 \) and \( x = -4 \).
The correct response is:
**x = 4, x = -4**.