Use completing the square to solve for x in the equation (x-12)(x+4)=9

Step-by-step explanation:

lets foil it and complete the square

x^2+4x-12x-48=9

x^2-8x=57

(-8/.5)^2=16

(x-4)^2-73

Choice d is the answer.

Step-by-step explanation:

We have given a  equation.

(x-12)(x+4) = 9

We have to find the solution using completing square technique.

Simplifying given given equation, we have

x²+4x-12x-48 = 9

Adding 48 to both sides of above equation, we have

x²-8x-48+48 =  9+48

x²-8x =  57

Adding the square of half of the term -8x to both sides of above equation, we have

x²-8x+(-4)² =  57+(-4)²

x²+2(1)(-4)+(-4)² =  57+16

(x-4)² = 73

Taking square root to both sides of above equation, we have

√(x-4)² = √73

x-4  = ±√73

Adding 4 to both sides of above equation, we have

x-4+4  =  ±√73+4

x  =  4±√73 which is the answer.

the correct answer is the second option

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.