Questions: 2r^2 - 25 = 0

Transcript text: $2 r^{2}-25=0$

Solution

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 $r$.

Step 1: Rearrange the Equation

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

Step 2: Solve for $r^2$

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

Step 3: Solve for $r$

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

Step 4: Simplify the Square Root

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

Step 5: Rationalize the Denominator

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

Step 6: Numerical Approximation

Calculate the numerical approximation: \[ r \approx \pm 3.5355 \]

Final Answer

The solutions to the equation are: \[ \boxed{r = 3.5355} \] \[ \boxed{r = -3.5355} \]

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