16x2−49=0

Question

Keep answer in fraction form. List smaller solution first.
x=

and

Answer 1

To solve the equation \( 16x^2 - 49 = 0 \), we can start by rearranging the equation:

\[ 16x^2 = 49 \]

Next, divide both sides by 16:

\[ x^2 = \frac{49}{16} \]

Now, take the square root of both sides:

\[ x = \pm \sqrt{\frac{49}{16}} \]

This simplifies to:

\[ x = \pm \frac{7}{4} \]

Thus, the two solutions are \( \frac{7}{4} \) and \( -\frac{7}{4} \).

Listing the smaller solution first, we have:

\[ x = -\frac{7}{4} \quad \text{and} \quad x = \frac{7}{4} \]