Final answer:
To complete the square for the equation x² + 8x, add 16 to both sides to get the perfect square trinomial (x + 4)². Solving (x + 4)² = 16 yields solutions x = 0 and x = -8.
Step-by-step explanation:
To complete the square for the equation x² + 8x = _, we must find a number that, when added to both sides of the equation, will transform the left-hand side into a perfect square trinomial. The process to determine this number is to take half the coefficient of x, which is 8 in this case, square it, and add it to both sides.
The number to add would thus be (8/2)² = 16.
Once 16 is added, the equation becomes x² + 8x + 16 = 16. The left-hand side is now a perfect square trinomial and can be written as (x + 4)². The equation then simplifies to (x + 4)² = 16. To solve for x, you would take the square root of both sides, yielding x + 4 = ±√16, which further simplifies to x + 4 = ±4. Finally, subtracting 4 from both possible scenarios, we find that x = 0 or x = -8.