Answer:
That (blank) is 9.
Explanation:
Please write 8x^2 - 48x = -104, with " ^ " indicating exponentiation. Thanks.
This sounds like a perfect example of "completing the square."
First, factor 8x^2 - 48x = -104: 8(x^2 - 6x = -13).
If we focus SOLELY on x^2 - 6x = -13, it's just a little easier to "complete the square." Take half of the coefficient of x (which here is -6), and square that result (which here is (-3)^2, or 9. Now add 9 both sides of x^2 - 6x = -13:
x^2 - 6x + 9 = -13 + 9. Note: The "blank" in the problem statement is 9.
We could go ahead and solve this, tho' we weren't asked to do so. Rewrite x^2 - 6x + 9 as (x - 3)^2:
x^2 - 6x = -13 then becomes (x - 3)^2 = 4. To solve for x, take the sqrt of both sides of this latest result, obtaining x - 3 = plus or minus 2. Add 3 to both sides to isolate x: x = 3 plus or minus 2.
Thus, x = 5 or x = 1.