What is the intermediate step in the form (x+a)^2=b as a result of completing the square for the following equation?

4x ^2 +47x+104=7x

1 answer

First, let's simplify the equation to make it easier to work with:
4x^2 + 47x + 104 - 7x = 0
This can be simplified to:
4x^2 + 40x + 104 = 0

The intermediate step in completing the square for this equation is to divide the entire equation by the coefficient of x^2, which is 4 in this case:
x^2 + 10x + 26 = 0

Now we can complete the square by adding the square of half of the coefficient of x, which is 5 in this case. Add (5^2) = 25 to both sides of the equation:
x^2 + 10x + 25 + 26 = 25
x^2 + 10x + 25 = -26

Next, we can rewrite the left side of the equation as a perfect square:
(x + 5)^2 = -26

This is the intermediate step after completing the square for the given equation.