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saw5 [17]
4 years ago
15

Find the roots of the quadratic equation x^2 – 8x = 9 by completing the square. Show your work

Mathematics
2 answers:
Butoxors [25]4 years ago
6 0

To solve by completing the square, you have to write the equation in the form x^2+2ax+a^2=(x+a)^2

Using 2ax=-8x, we can solve for a, which is 2ax/2x. We can then use this to find that a=-4.

Plug a=-4 into the equation x^2+2ax+a^2=(x+a)^2.

x^2-8x+(-4)^2=9+(-4)^2

x^2-8x+(-4)^2=25

Complete the square:

(x-4)^2=25

Solve x-4=sqrt25 (square root) and x-4=negsqrt25 (negative square root)

x=9 and x=-1.

These can be proven by plugging them into the above equation (x-4)^2=25.

9-4^2=25 and -1-4^2=25.

Hope this helps ;)

worty [1.4K]4 years ago
5 0

x^2  -  8x = 9

Add both sides the square of half of 8 , that is {(\frac{8}{2})} ^2

x^2  -  8x  + (\frac{8}{2})^2 = 9 +(\frac{8}{2})^2(x^2 -8x +4^2 ) = 9 +16

(x-4)^2 = 25

Take square root on both sides

x-4 = 5 or x-4 = -5

⇒ x= 9 or x= -1

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Answer:

700 dollars.

Step-by-step explanation:

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7 0
3 years ago
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Using​ 45-in. fabric, Regan needs 2 and one fourth yd for a​ dress, one fourth yd of contrasting fabric for the band at the​ bot
Arte-miy333 [17]

Answer:

7\dfrac14$ yards

Step-by-step explanation:

Regan needs the following:

2\dfrac{1}{4} yards for a​ dress

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Total Length of fabric needed

= 2\dfrac{1}{4}+\dfrac{1}{4}+4\dfrac{3}{4}\\=2+4+\dfrac{1}{4}+\dfrac{3}{4}+\dfrac{1}{4}\\=6+1+\dfrac{1}{4}\\=7\dfrac{1}{4}$ yards

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4 0
3 years ago
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choli [55]

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Step-by-step explanation:

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Match the mean, median, mode, and range for the data set below. 2, 7, 8, 4, 8, 2, 5, 5, 7, 2
dusya [7]

Answer:

Mean - 5

Median - 5

Mode - 2

Range - 6

Step-by-step explanation:

Mean-

If you add 2 + 7 + 8 + 4 + 8 + 2+ 5+ 5+ 7 +2= 50

50 divided by 10 (the amount of numbers in the equation) = 5 for the mean

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3 years ago
(3x - 2)^5 =(3x - 2)^2
andreyandreev [35.5K]

Answer:

x=3/2,1

Step-by-step explanation:Given

(3x-2)ˆ5-(3x-2)ˆ2=0

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(3x-2)ˆ2{(3x-2)ˆ3-1}=0

(3x-2)ˆ2=0 Or (3x-2)ˆ3-1=0

3x-2=0 Or(3x-2)ˆ3=1

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