Question

When completing the square for x²-18x+___=77, which equation is a correct step in the process?

1) x²-18x+81=77
2) x²-18x+9=77
3) x²-18x-9=77
4) x²-18x-81=77

Answer 1

To complete the square for the equation x² - 18x + ___ = 77, the correct step is to add the square of half the coefficient of x, which is 9.

Step-by-step explanation:

To complete the square for the equation x² - 18x + ___ = 77, we need to find the missing term that will make it a perfect square trinomial. The correct step in the process is option 2) x² - 18x + 9 = 77. Here's how we can determine this:

1. Start with the given equation: x² - 18x + ___ = 77
2. Take half of the coefficient of x (-18) and square it: (-18/2)² = (-9)² = 81
3. Add the squared value to both sides of the equation: x² - 18x + 9 = 77 + 81
4. Combine like terms: x² - 18x + 9 = 158