Question

Solve the quadratic equation using factoring 49x^2−225=0
.(1 point)
Responses

x=−715, x=715
x=−715, x=715

x=−22549, x=22549
x=−22549, x=22549

x=−157
x is equal to negative 15 sevenths

x=−157, x=157

Answer 1

To solve the quadratic equation \( 49x^2 - 225 = 0 \) using factoring, we can begin by rearranging it into a standard form.

1. **Rearrange the equation**: We can see that the left-hand side can be factored as a difference of squares:
\[
49x^2 - 225 = (7x)^2 - 15^2
\]
So, we can write:
\[
(7x - 15)(7x + 15) = 0
\]

2. **Set each factor to zero**:
\[
7x - 15 = 0 \quad \text{or} \quad 7x + 15 = 0
\]

3. **Solve for \( x \)**:
- For the first equation:
\[
7x - 15 = 0 \implies 7x = 15 \implies x = \frac{15}{7}
\]
- For the second equation:
\[
7x + 15 = 0 \implies 7x = -15 \implies x = -\frac{15}{7}
\]

Thus, the solutions are:
\[
x = -\frac{15}{7}, \quad x = \frac{15}{7}
\]

From the provided options, the correct response is:
**x = -157, x = 157** (which corresponds to **x = -\frac{15}{7} and x = \frac{15}{7}**).