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3 years ago

Solve by completing the square. x^2 + 4x – 1= 0

Mathematics

1 answer:

NNADVOKAT [17]3 years ago

8 0

Answer:

x = -2 ± sqrt(5)

Step-by-step explanation:

x^2 + 4x – 1= 0

Add 1 to each side

x^2 + 4x – 1+1= 0+1

x^2 +4x = 1

Take the coefficient of x

Divide by 2

4/2 =2

Square it

2^2=4

Add it to each side

x^2 +4x+4=1+4

(x+2)^2 = 5

Take the square root of each side

sqrt((x+2)^2 )=± sqrt(5)

x+2 = ± sqrt(5)

Subtract 2 from each side

x+2-2 = -2 ± sqrt(5)

x = -2 ± sqrt(5)

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The true statement is (a) If material 2 is used, Carrie will earn a profit if she sells chairs for more than $150 each.

<h3>How to determine the true profit functions</h3>

From the complete questions, the profit functions are calculated as follows:

<u>Material 1</u>

$P(x) = 5000000- 20000x - 200000x + 2000x^2$

$P(x) = 5000000-220000x + 2000x^2$

<u>Material 2</u>

$P(x) = 4000000 - 10000x - 160000x+ 1000x^2$

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$P(x) = 2000000 - 5000x - 54000x - 270x^2$

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Next, we test the options

Option 1: When material 2 is used

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Calculate P(151) using $P(x) = 4000000-170000x+ 1000x^2$

So, we have:

$P(151) = 4000000-170000 * 151+ 1000* 151^2$

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Option 2: When material 1 is used

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Calculate P(49) using $P(x) = 5000000-220000x + 2000x^2$

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$P(30) = 4000000-170000*30+ 1000*30^2$

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