Final answer:
No additional value is needed to complete the square for the equation x^2 - 20 = 96, as the equation x^2 - 20 + 20 = 96 + 20 simplifies to x^2 = 116, where x^2 is already a perfect square.
Step-by-step explanation:
The student has asked what value completes the square for the equation x2 - 20 = 96. To complete the square, we must form a perfect square trinomial on the left side of the equation. First, we would add 20 to both sides of the equation to balance it:
x2 = 116
Next, we take the coefficient of the x-term (which is 0 in this case since there is no x-term), halve it, and then square the result to find the value that completes the square. However, since there is no x-term, we do not need to add any value to make it a perfect square; x2 is already a perfect square. Therefore, no additional value is needed to complete the square for the equation x2 - 20 = 96, as the left side is already a perfect square (x2).