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

Explanation:

Step1: Rearrange the equation

First, move all terms to one - side of the equation: [2x^{2}+8x-(x^{2}-16)=0] [2x^{2}+8x - x^{2}+16 = 0] [x^{2}+8x + 16=0]

Step2: Factor the quadratic equation

The quadratic equation (x^{2}+8x + 16) is a perfect - square trinomial of the form (a^{2}+2ab + b^{2}=(a + b)^{2}), where (a=x) and (b = 4). So, (x^{2}+8x + 16=(x + 4)^{2}=0)

Step3: Solve for x

Set (x + 4=0) [x=-4]

Answer:

(-4)