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

Solution:

Given equation is 2x² + 8x = x² - 16

We can write it as 2x² - x² + 8x + 16 = 0

=> x² + 8x + 16 = 0

This is a quadratic equation in x

x² + 4x + 4x + 16 = 0

x(x + 4) + 4(x + 4) = 0

(x + 4)(x + 4) = 0

x = 4, 4

Therefore, the solution for the given equation is 4, 4.

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

Summary:

The only solution of 2x² + 8x = x² - 16 is 4.