A) Grant was asked to solve 49x

Question

2 − 225 = 0 by factoring using the difference of squares pattern.
What is/are the correct solution(s)? (1 point)
x = −
15
7
x =
225
49
, x = −
225
49
x = −
15
7
, x =
15
7
x = −
7
15
, x =
7
15

Answer 1

To solve the equation \(49x^2 - 225 = 0\) using the difference of squares pattern, we can first express the equation as a difference of squares:

\[ 49x^2 - 225 = (7x)^2 - 15^2 = 0 \]

Next, we can factor it as follows:

\[ (7x - 15)(7x + 15) = 0 \]

Now we can set each factor equal to zero:

1. \(7x - 15 = 0\)
2. \(7x + 15 = 0\)

Solving the first equation:

\[ 7x - 15 = 0 \implies 7x = 15 \implies x = \frac{15}{7} \]

Solving the second equation:

\[ 7x + 15 = 0 \implies 7x = -15 \implies x = -\frac{15}{7} \]

Therefore, the solutions to the equation \(49x^2 - 225 = 0\) are:

\[ x = \frac{15}{7}, \quad x = -\frac{15}{7} \]

So the correct answers from your options are:

• \(x = -\frac{15}{7}\)
• \(x = \frac{15}{7}\)