Question

When solving x2 + 14x + 9 = 0 by completing the square, which of the following is a step in the process?

(x − 7)2 = 58

(x − 7)2 = 40

(x + 7)2 = 58

(x + 7)2 = 40

Note: the "2" are exponents

Answer 1

First: a bit of housekeeping. Please denote exponentiation by using the symbol " ^ " or by drawing your input:

Answer 2

Thank You ive been stuck on this for quite sometime.

Answer 3

Complete the square: x2 + 14x + 9 = 0

Look at the coefficient of the x term. it's 14. Take HALF of this coefficent, obtaining 7, and square that: Result is 49. Add, and then immediately subtract, 49 in the given equation.

Answer 4

Thus,\[x^2+14x+9 \]

Answer 5

becomes \[x^2 + 14x +(7)^2 - (7)^2 + 9 =0\]

Answer 6

Now ask yourself: What is the square root of the expression given by the first 3 terms?

Express that as a perfect square, using " ^ " to denote exponentiation.

Does this help you decide which of the four possible answers is the correct one? Hope so.

Answer 7

It does thank you !

Answer 8

Great!!

Then,\[(x+7)^2 - 49 +9 = 0\]

Answer 9

combine the -49 and the 9 to get what?
Move this result to the right side of your equation.
Take the square root of the left side, then the square root of the right side, being sure to write "plus or minus" in front of that 40, on the right side.

You weren't asked to solve this problem, but it'd be worth doing so for the practice.

Answer 10

Ah, Warren, I see you also do the "split 0 into its positive and negative sides" approach that I use :-)