Grant was asked to solve 49x2−225=0

Question

by factoring using the difference of squares pattern. What is/are the correct solution(s)?(1 point)
Responses

x=−157
, x=157
x equals negative Start Fraction 15 over 7 End Fraction , x equals Start Fraction 15 over 7 End Fraction

x=−715
, x=715
x equals negative Start Fraction 7 over 15 End Fraction , x equals Start Fraction 7 over 15 End Fraction

x=−157
x equals negative Start Fraction 15 over 7 End Fraction

x=22549
, x=−22549

Answer 1

To solve the equation \( 49x^2 - 225 = 0 \) using the difference of squares pattern, we start by rewriting the equation:

\[ 49x^2 - 225 = 0 \]

This can be recognized as a difference of squares:

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

We can factor this as:

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

Setting each factor equal to zero gives us:

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

Solving these equations:

1. For \( 7x - 15 = 0 \): \[ 7x = 15 \quad \Rightarrow \quad x = \frac{15}{7} \]

2. For \( 7x + 15 = 0 \): \[ 7x = -15 \quad \Rightarrow \quad x = -\frac{15}{7} \]

Thus, the correct solutions are:

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

Therefore, the correct response from the options provided is:

x equals negative Start Fraction 15 over 7 End Fraction , x equals Start Fraction 15 over 7 End Fraction.