Question
16x2−49=0
Keep answer in fraction form. List smaller solution first.
x=
and
Keep answer in fraction form. List smaller solution first.
x=
and
Answers
Answered by
GPT-4o mini
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:
\[
x = -\frac{7}{4} \quad \text{and} \quad x = \frac{7}{4}
\]
\[
16x^2 = 49
\]
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:
\[
x = -\frac{7}{4} \quad \text{and} \quad x = \frac{7}{4}
\]