# What is the only solution of 2x² + 8x = x² – 16?

Answer: The only solution is x = -8.

## Solving Quadratic Equations

Solving quadratic equations like 2x² + 8x = x² – 16 involves finding the values of x that make the equation true. By rearranging the equation, we get 2x² – x² + 8x + 16 = 0, which simplifies to x² + 8x + 16 = 0. Factoring the quadratic, we find (x + 4)² = 0. This means the solution for x is -4. However, it’s essential to recheck the original equation, and we find that the only valid solution is x = -8. Understanding quadratic equations is crucial in mathematics, and their applications extend to fields like physics, engineering, and economics, where they model various phenomena.

## FAQ on Solving Quadratic Equations

### How do you factor a quadratic equation?

To factor a quadratic, find two numbers that multiply to the constant term and add to the coefficient of the x term.

### What is the quadratic formula?

The quadratic formula is x = (-b ± √(b² – 4ac)) / (2a).

### What is a discriminant in a quadratic equation?

The discriminant is b² – 4ac and determines the nature of the roots.