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

Move all terms to one side

2x^2 + 8x - x^2 + 16 = 0

Simplify 2x^2 + 8x - x^2 + 16 to x^2 + 8x + 16

x^2 + 8x + 16 = 0

Rewrite x^2 + 8x + 16 in the form a^2 + 2ab + b^2, where a = x and b = 4

x^2 + 2 (x) (4) + 4^2 = 0

Use the Square of Sum: (a + b) = a^2 + 2ab + b^2

(x + 4) ^2 = 0

Take the square root of both sides

x + 4 = 0

Subtract 4 from both sides

x = - 4