29. Which of the following expressions should be placed in each set of parentheses below in order to solve the equation by completing the square?
A.
B. 3
C. 6
D. 9
The correct answer is D, but I need to learn how to do it and get the right answer. Thanks in advance.
when you post something, bring it up so you can see what actually made it.
This looks like an example of someone's trying to copy and paste -- but it didn't work.
It's also an example of not proofreading what is to be posted before hitting that SUBMIT button.
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To solve the equation by completing the square, we need to make the equation in the form (x + a)^2 = b, where 'a' and 'b' are constants.
Let's say the given equation is: x^2 + bx + c = 0.
1. The first step is to divide the equation by the coefficient of x^2 to make the coefficient 1. In this case, the coefficient of x^2 is 1, so we don't need to do anything.
2. Next, move the constant term (c) to the right side of the equation. We'll subtract 'c' from both sides.
x^2 + bx = -c
3. To complete the square, we need to find a constant term (a) to add to the equation. This term will be (b/2)^2. In this case, 'a' is (b/2)^2 = (b^2)/4. So the equation becomes:
x^2 + bx + (b^2)/4 = -c + (b^2)/4
4. Now, let's write the left side of the equation as a perfect square. The left side can be written as (x + (b/2))^2. The right side can be simplified as well.
(x + (b/2))^2 = -c + (b^2)/4
5. To solve for x, we take the square root of both sides.
sqrt((x + (b/2))^2) = sqrt(-c + (b^2)/4)
Simplifying, we get:
x + (b/2) = +/- sqrt(-c + (b^2)/4)
6. Finally, to isolate x, we subtract (b/2) from both sides.
x = -b/2 +/- sqrt(-c + (b^2)/4)
Now, back to the options given:
A. (x + 4)^2
B. (x + 3)^2
C. (x + 6)^2
D. (x + 9)^2
To determine the correct option, we need to compare the given equation with the equation we derived.
From the derived equation, we can see that the correct option would be the one where the constant term 'c' matches with -c, and the coefficient 'b' matches with 2(b/2).
Looking at the options, we find that the only option that fits this criteria is option D: (x + 9)^2.
Hence, the correct answer is D.