Grant was asked to solve 49x2−225=0 by factoring using the difference of squares pattern. What is/are the correct solution(s)?(1 point)

Question

Responses

x=−715, x=715
x is equal to negative 7 over 15, x is equal to 7 over 15 - no response given

x=−157
x is equal to negative 15 sevenths - no response given

x=−157, x=157
x is equal to negative 15 sevenths, x is equal to 15 sevenths - no response given

x=225/49, x=−225/49

Answer 1

To solve the equation \( 49x^2 - 225 = 0 \) using the difference of squares pattern, we can rewrite it in the form of \( a^2 - b^2 = 0 \).

Here, we have:

• \( a^2 = 49x^2 \) can be expressed as \( (7x)^2 \)
• \( b^2 = 225 \) can be expressed as \( 15^2 \)

So, we can rewrite the equation as:

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

This can be factored using the difference of squares formula, which is \( a^2 - b^2 = (a - b)(a + b) \):

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

To find the solutions, we can set each factor equal to zero:

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

   • Solving for \( x \): \[ 7x = 15 \implies x = \frac{15}{7} \]

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

   • Solving for \( x \): \[ 7x = -15 \implies x = -\frac{15}{7} \]

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

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

Therefore, the correct response will be:

x is equal to negative 15 sevenths, x is equal to 15 sevenths.