Final answer:
To find the intermediate step in the form (x+a)^2=b for completing the square of the equation -5x^2 - 70x - 280 = 10, we isolate the x terms, scale the equation, complete the square, and end up with the intermediate form (x+7)^2=-9.
Step-by-step explanation:
The intermediate step in the form (x+a)^2=b when completing the square for the equation -5x^2 - 70x - 280 = 10 involves several steps.
First, we need to add 280 to both sides of the equation to isolate the quadratic and linear terms on one side, resulting in -5x^2 - 70x = 290.
To have a coefficient of 1 for the x^2 term, we divide the equation by -5, which gives us x^2 + 14x = -58.
Next, we find the constant term to add to both sides to complete the square, which is (b/2)^2 where b is the coefficient of x.
In this case, (14/2)^2 equals 49. Add 49 to both sides to complete the square, resulting in x^2 + 14x + 49 = -58 + 49, simplifying to (x + 7)^2 = -9.
Therefore, the intermediate step in the form (x+a)^2=b is (x+7)^2=-9.