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BaLLatris [955]
3 years ago
10

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

Mathematics
2 answers:
ExtremeBDS [4]3 years ago
5 0

Answer:

x = 4 + √73

Step-by-step explanation:

The given equation is ( x-12 ) ( x + 4 ) = 9

We will solve the equation first.

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

x( x+4 ) - 12 ( x + 4 ) = 9 [ Distributive property ]

x² + 4x - 12x - 48 = 9

x² - 8x - 48 = 9

x² - 8x - 48 - 9 = 0

x² - 8x - 57 = 0

[ x² - 2 (4x) + 16 ] - 57 - 16 = 0

(x - 4)² - 73 = 0

(x - 4)² = 73

( x-4 )² = √73

x = 4 + √73

x = 4 + √73 is the answer.

Vladimir79 [104]3 years ago
3 0
Hello!

You can multiply (x-12) and (x+4)

x * x = x^2
x * 4 = 4x
-12 * x = -12x
-12 * 4 = -48

Now we have

x^2 - 8x - 48 = 9

Subtract 9 from both sides

x^2 - 8x -57 = 0

Use the quadratic formula

This give use the answer of

x = 4 +\sqrt{72}

Hope this helps!
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7 0
2 years ago
A rectangular parking area measuring 5000 ft squared is to be enclosed on three sides using​ chain-link fencing that costs ​$5.5
kaheart [24]

Answer:

Dimensions: 75.3778 ft and 66.3325 ft

Minimum price: $1658.31

Step-by-step explanation:

Let's call the length of the parking area 'x', and the width 'y'.

Then, we can write the following equations:

-> Area of the park:

x * y = 5000

-> Price of the fences:

P = 2*x*5.5 + y*5.5 + y*7

P = 11*x + 12.5*y

From the first equation, we have that y = 5000/x

Using this value in the equation for P, we have:

P = 11*x + 12.5*5000/x = 11*x + 62500/x

To find the minimum of this function, we need to take its derivative and then make it equal to zero:

dP/dx = 11 - 62500/x^2 = 0

x^2 = 65000/11

x = 250/sqrt(11) = 75.3778 ft

This is the x value that gives the minimum cost.

Now, finding y and P, we have:

x*y = 5000

y = 5000/75.3778 = 66.3325

P = 11*x + 62500/x = $1658.31

5 0
3 years ago
Which inequality will have a solid boundary line and a shaded region above its graph? x − y ≥ 3 2x − 3y ≤ 3 3y − x < 2 2x + y
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7 0
3 years ago
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marissa [1.9K]

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What is the GCF of 48m5n and 81m2n2?
Lady bird [3.3K]
To find the GCF of the two terms, continuous division must be done.
What can be used to divide both terms such that there is not a remainder?
Start small, let's take 2. It could be a GCF.
Move up higher, say 3. Yes, it can be a GCF.
To see if there might be a greater common factor, divide the constants by 3.
48/3 = 16
81/3 = 27
Upon inspection and contemplation, there is no more common factor between 16 and 27. So, 3 is the GCF.

Moving on, when it comes to variables. The variable with the least exponents is easily the GCF. For the variable m, the GCF is m2 and for n, the GCF is n.

Combining the three, we have the overall GCF = 3m2n
7 0
3 years ago
Read 2 more answers
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