To find the intermediate step in completing the square for the equation x² - 126 = 2x + 1, we first need to rearrange the equation so that the x terms are on one side and the constant terms are on the other side. Here's the step-by-step process:
1. Move the constant term (-126) to the right side by adding 126 to both sides:
x² = 2x + 127
2. To complete the square, we want the coefficient of x to be 1. Divide the entire equation by the coefficient of x (which is 2):
(1/2)x² = x + 63.5
3. Now, we focus on the right side of the equation and isolate the constant term (63.5). To complete the square, we take half of the coefficient of x (which is 1) and square it. Half of 1 is 0.5, and 0.5 squared is 0.25. Add 0.25 to both sides of the equation:
(1/2)x² + 0.25 = x + 63.5 + 0.25
(1/2)x² + 0.25 = x + 63.75
The intermediate step in completing the square for the equation x² - 126 = 2x + 1 is:
(1/2)x² + 0.25 = x + 63.75
