Question

What is the intermediate step in the form (x+a)²=b as a result of completing the square for the following question. -4x²-83x=-3x+396

Answer 1

To complete the square of the equation -4x²-83x=-3x+396, we rearrange it, divide by -4, and then add the square of half the coefficient of x to both sides to get (x+10)²=1 as the intermediate step.

Step-by-step explanation:

To solve the quadratic equation -4x²-83x=-3x+396 by completing the square, we follow these steps:

1. First, we move all the terms involving x to one side and the constant term to the other side to get -4x²-80x=396.
2. Next, we divide through by the coefficient of the x² term, which is -4, to obtain x²+20x=-99.
3. After that, we find the value to complete the square for the x term, which is (20/2)² = 100, and add it to both sides to get x²+20x+100 = -99+100.
4. This gives us the perfect square (x+10)²=1. The intermediate step in the form (x+a)²=b has been found, and it is (x+10)²=1.