Solve for s.

Question

4s^2–49=0
Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

Answer 1

To solve the equation \( 4s^2 - 49 = 0 \), we can first isolate the \( s^2 \) term:

1. Add 49 to both sides: \[ 4s^2 = 49 \]

2. Next, divide both sides by 4: \[ s^2 = \frac{49}{4} \]

3. Now take the square root of both sides. Remember that taking the square root yields both a positive and a negative solution: \[ s = \pm \sqrt{\frac{49}{4}} \] \[ s = \pm \frac{\sqrt{49}}{\sqrt{4}} = \pm \frac{7}{2} \]

Thus, the solutions are: \[ s = \frac{7}{2}, -\frac{7}{2} \]

In summary, the solutions are: \[ \frac{7}{2}, -\frac{7}{2} \]