Questions: 2r^2 - 25 = 0

Solution Steps

To solve the equation $2r^2 - 25 = 0$, we need to isolate $r$. First, add 25 to both sides to get $2r^2 = 25$. Then, divide both sides by 2 to solve for $r^2$. Finally, take the square root of both sides to find the values of $r$.

Start with the equation $2r^2 - 25 = 0$. Add 25 to both sides to get: $$2r^2 = 25$$

Divide both sides by 2 to isolate $r^2$: $$r^2 = \frac{25}{2}$$

Take the square root of both sides to solve for $r$: $$r = \pm \sqrt{\frac{25}{2}}$$

Simplify $\sqrt{\frac{25}{2}}$: $$r = \pm \frac{\sqrt{25}}{\sqrt{2}} = \pm \frac{5}{\sqrt{2}}$$

Rationalize the denominator: $$r = \pm \frac{5 \cdot \sqrt{2}}{2}$$

Calculate the numerical approximation: $$r \approx \pm 3.5355$$

Final Answer