what is the solution to 2x²+8x=x² - 16?\n○ x=-4\n○ x=-2\n○ x=2\n○ x=4

Explanation:

Step1: Rearrange the equation

Move all terms to one - side: $2x^{2}+8x-(x^{2}-16)=0$ $2x^{2}+8x - x^{2}+16 = 0$ $x^{2}+8x + 16=0$

Step2: Factor the quadratic equation

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

Step3: Solve for x

Take the square - root of both sides: $x+4 = 0$ $x=-4$

Answer:

A. $x=-4$