We are given original equation: 
We need to find the enter and radius of a circle using the completing the square method.
The steps are as following :
Step 1 [original equation]: x^2 − 10x + y^2 + 12y = 20 .
Step 2 [group like terms]: (x^2 − 10x) + (y^2 + 12y) = 20
Step 3 [complete the quadratics]: (x^2 − 10x + 25) + (y^2 + 12y + 36) = 20 + (25 + 36).
Step 4 [simplify the equation]: (x^2 − 10x + 25) + (y^2 + 12y + 36) = 64.
Step 5 [factor each quadratic]: (x − 5)^2 + (y + 6)^2 = 8^2
Step 6 [identify the center and radius]: Center = (5, −6) Radius = 8.
<h3>Step 6 is incorrect.</h3><h3>The center should be (5,-6).</h3><h3> Replace − 5 with + 5 and replace + 6 with − 6.</h3>
Answer:
x^2 -x -2
Step-by-step explanation:
Use polynomial long division.
0 + x^2 -x -2
___________________________________
(2x+3) | 2x^3 +x^2 -7x -6
-2x^3 -3x^2
_________
-2x^2 -7x
+2x^2 +3x
__________
-4x -6
+2x +6
_______
0
Suppose the dimensions of the rectangle is x by y and let the side enclosed by a house be one of the sides measuring x, then the sides that is to be enclosed are two sides measuring y and one side measuring x.
Thus, the length of fencing needed is given by
P = x + 2y
The area of the rectangle is given by xy,
i.e.
Substituting for y into the equation for the length of fencing needed, we have
For the amount of fencing to be minimum, then
Now, recall that
Thus, the length of fencing needed is given by
P = x + 2y = 24 + 2(12) = 24 + 24 = 48.
Therefore, 48 feets of fencing is needed to enclose the garden.
