To find the sum of the roots of the quadratic equation \(2x^2 - 5 = -3\), we first need to rearrange the equation to its standard form, \(ax^2 + bx + c = 0\).

### Step 1: Rearrange the equation
Starting with the given equation:
\[
2x^2 - 5 = -3
\]

Add 3 to both sides to move all terms to one side:
\[
2x^2 - 5 + 3 = 0
\]

Simplify:
\[
2x^2 - 2 = 0
\]

### Step 2: Factor or solve for roots
The equation simplifies to:
\[
2(x^2 - 1) = 0
\]
\[
x^2 - 1 = 0
\]

This is a difference of squares, so it factors as:
\[
(x - 1)(x + 1) = 0
\]

### Step 3: Solve for the roots
Set each factor equal to zero:
\[
x - 1 = 0 \quad \text{or} \quad x + 1 = 0
\]
\[
x = 1 \quad \text{or} \quad x = -1
\]

### Step 4: Sum of the roots
The sum of the roots is:
\[
1 + (-1) = 0
\]

So, the sum of the roots is **0**.

Would you like any further details or have any other questions?

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Here are 5 related questions:
1. What is the product of the roots of the equation \(2x^2 - 5 = -3\)?
2. How would the sum of the roots change if the equation was \(2x^2 - 5x - 3 = 0\)?
3. Can you find the roots of the equation \(x^2 - 4x + 3 = 0\) and their sum?
4. How does the sum of the roots relate to the coefficients in a quadratic equation?
5. What are the implications if the sum of the roots of a quadratic equation is zero?

**Tip:** The sum of the roots of a quadratic equation in the form \(ax^2 + bx + c = 0\) is given by \(-\frac{b}{a}\).

Learn how to find the sum of the roots for the quadratic equation 2x² - 5 = -3. This detailed guide walks through the step-by-step solution, including rearranging the equation to standard form and applying the sum of roots formula. Ideal for students in Grades 9-10.

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