To solve the equation \(49x^2 - 225 = 0\) using the difference of squares pattern, we can first recognize that this expression fits the form \(a^2 - b^2 = 0\) where:
- \(a^2 = 49x^2\) (so \(a = 7x\))
- \(b^2 = 225\) (so \(b = 15\))
We can rewrite the equation as:
\[ (7x)^2 - (15)^2 = 0 \]
Using the difference of squares formula, \(a^2 - b^2 = (a - b)(a + b)\), we can factor this as:
\[ (7x - 15)(7x + 15) = 0 \]
Next, we set each factor equal to zero:
- \(7x - 15 = 0\)
- \(7x + 15 = 0\)
Solving for \(x\) in each equation:
-
From \(7x - 15 = 0\): \[ 7x = 15 \implies x = \frac{15}{7} \]
-
From \(7x + 15 = 0\): \[ 7x = -15 \implies x = -\frac{15}{7} \]
Thus, the solutions to the equation \(49x^2 - 225 = 0\) are:
\[ x = \frac{15}{7}, \quad x = -\frac{15}{7} \]
Now, looking at the given responses, we can see that the correct solutions are:
- \(x = -\frac{15}{7}\)
- \(x = \frac{15}{7}\)
Therefore, the correct choice is:
x=−15/7, x=15/7.