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To solve the quadratic equation:

\[
2x^2 - 45 = 0
\]

we need to find the values of \(x\) that satisfy this equation.

### Step 1: Isolate \(x^2\)
Divide the entire equation by 2 to simplify:

\[
x^2 - \frac{45}{2} = 0
\]

\[
x^2 = \frac{45}{2}
\]

### Step 2: Take the square root of both sides
To solve for \(x\), take the square root of both sides:

\[
x = \pm \sqrt{\frac{45}{2}}
\]

### Step 3: Simplify the square root
We can simplify \(\sqrt{\frac{45}{2}}\) by breaking it down:

\[
\sqrt{\frac{45}{2}} = \sqrt{\frac{9 \cdot 5}{2}} = \frac{3\sqrt{10}}{\sqrt{2}} = \frac{3\sqrt{10} \cdot \sqrt{2}}{2} = \frac{3\sqrt{5}}{2}

Solve the quadratic equation 2x^2 - 45 = 0.

Learn how to solve the quadratic equation 2x^2 - 45 = 0 by isolating x and applying the square root method. This step-by-step solution includes simplifying square roots and is suitable for students in Grades 7-9.

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