Question

To solve by completing the square, what needs to be moved in this equation?

x2 = 9 - 4x


A. A = 4, b = 8, c= - 3


B. A = 4, b = - 8, c = - 3


C. A = 4, b = 8, c = 3


D. A = 4, b = - 8, c = 3

Answer 1

Explanation:

To solve by completing the square, we need to have the equation in the form:

(x - h)^2 = k

where h and k are constants. To get the equation in this form, we need to move the constant term to the right side and group the x terms together. So let's start by moving 9 to the right side:

x^2 + 4x = 9

Next, we need to add and subtract a constant term that will allow us to complete the square. The term we need to add is (b/2a)^2, where a is the coefficient of x^2 and b is the coefficient of x. In this case, a = 1 and b = 4, so (b/2a)^2 = (4/2)^2 = 4. So we add and subtract 4:

x^2 + 4x + 4 - 4 = 9

Now we can group the first three terms and simplify:

(x + 2)^2 - 4 = 9

Add 4 to both sides:

(x + 2)^2 = 13

So the answer is not given in any of the options provided.