The first few steps in solving the quadratic equation 9x2 + 49x = 22 − 5x by completing the square are shown. 9x2 + 49x = 22 − 5

The correct answer is C. 100

Hello!

(x+a)·(x+b) equals x²+xa+xb+ab which simplifies to x²-12x-45

x² equals x²
xa+xb can be expressed as (a+b)x = -12x thus, (a+b) = -12
ab equals -45

Under what conditions do (a+b) equal -12 and ab equal -45?

+3-15 results in -12 while (+3)(-15) gives -45
-3-15 yields -18 and (-3)(-15) results in +45
+3+15 produces +18 and (+3)(+15) also equal to +45
-3+15 equals +12 and (-3+15) results in -45

Conclusion:

(x+3)(x-15) 

Response:

The number 40 can be found in Pattern B. Additionally, following the rule, each sequence will expand.

Detailed breakdown:

Let’s build each sequence. Recall that the guideline is to "add 15" to generate each sequence starting from the provided initial number.

Pattern A.

Pattern B.

Pattern C.

You can see that the number 40 appears in Pattern B. Moreover, per the rule, each pattern will show an increase.