Quadratic Equations Online Practice

Question

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Question
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)
Responses

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

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

x=22549
, x=−22549
x equals Start Fraction 225 over 49 End Fraction , x equals negative Start Fraction 225 over 49 End Fraction
Remaining Attempts : 3

Answer 1

To solve the equation \(49x^2 - 225 = 0\) using the difference of squares pattern, we start by recognizing that it can be expressed in the form \(a^2 - b^2 = 0\), where \(a = 7x\) and \(b = 15\).

We can rewrite the equation as:

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

Using the difference of squares factorization, we can express it as:

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

Setting each factor to zero gives us two equations to solve:

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

Now, solving each equation:

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

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

Thus, the solutions are \(x = \frac{15}{7}\) and \(x = -\frac{15}{7}\).

Looking at the response options you’ve provided, the correct response is:

x = −15/7, x = 15/7.

(Note: Ensure to match the exact response formatting as it may vary.)