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 $-\frac{b}{a}$.