what is the solution to 2x²+8x=x² - 16?\no x=-4\no x=-2\no x=2\no 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, $x^{2}+8x + 16=(x + 4)^{2}=0$

Step3: Solve for x

If $(x + 4)^{2}=0$, then $x+4 = 0$. $x=-4$

Answer:

$x=-4$