Question

Consider 8x2 - 48x = -104. Write the equation so that x2 – 6x + (blank) = –13 + (blank)

Answer 1

Answer:

That (blank) is 9.

Step-by-step 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.  

Answer 2

Write the equation so that:

-6 and -13

Complete the square:

9 and 9

Hope this helps for Edg.