Solve the quadratic equation $25p^2 = 49$ by applying the factoring method.

Step 1 — Write in standard form. Subtract $49$ from both sides: $25p^2 - 49 = 0$

Step 2 — Factor the quadratic expression. The binomial is a difference of squares. $(5p - 7)(5p + 7) = 0$

Step 3 — Apply the Zero Product Property. Set each factor equal to zero: $5p - 7 = 0 \quad \text{or} \quad 5p + 7 = 0$

Step 4 — Solve each linear equation: $p = \frac{7}{5} \quad \text{or} \quad p = -\frac{7}{5}$

Step 5 — Check both solutions by substituting into the original equation $25p^2 = 49$: For $p = \frac{7}{5}$: $25\left(\frac{7}{5}\right)^2 = 25\left(\frac{49}{25}\right) = 49$ ✓ For $p = -\frac{7}{5}$: $25\left(-\frac{7}{5}\right)^2 = 25\left(\frac{49}{25}\right) = 49$ ✓ The solutions are $p = \frac{7}{5}$ and $p = -\frac{7}{5}$.