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2 years ago

X^2-6x+1=0 solve by completing square

Mathematics

2 answers:

asambeis [7]2 years ago

8 0

Answer:

x = 3 ± 2 $\sqrt{2}$

Step-by-step explanation:

x² - 6x + 1 = 0 ( subtract 1 from both sides )

x² - 6x = - 1

to complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 3)x + 9 = - 1 + 9

(x - 3)² = 8 ( take square root of both sides )

x - 3 = ± $\sqrt{8}$ = ± 2 $\sqrt{2}$ ( add 3 to both sides )

x = 3 ± 2 $\sqrt{2}$

Harrizon [31]2 years ago

5 0

The answer is x= +- 2 square root of 2 + 3

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mars1129 [50]

Answer:

$1.\:2^x=64, x=\boxed{6},\\2.\:x=\left(\frac{2}{3}\right)^3,x=\boxed{\frac{8}{125}}\\3.\:3\cdot (3^4)=3^x, x=\boxed{5}\\4.\:\frac{16}{25}=x^2,x=\boxed{\frac{4}{5}},$

Step-by-step explanation:

$1.\\\\2^x=64,\\\log 2^x=\log64,\\x\log 2=\log 64,\\x=\frac{\log 64}{\log 2}=\boxed{6}$

$2.\\x=\left(\frac{2}{5}\right)^3=\frac{2^3}{5^3}=\boxed{\frac{8}{125}}$

3. This problem incorporates an exponent property.

Exponent property used: $a^b\cdot a^c=a^{(b+c)}$ , yielding an answer of $\boxed{5}$

$4.\\\\\frac{16}{25}=x^2,\\x=\sqrt{\frac{16}{25}}=\frac{\sqrt{16}}{\sqrt{25}}=\boxed{\frac{4}{5}}$

3 0

3 years ago

Read 2 more answers

There are 4 jacks and 13 clubs in a standard, 52-card deck of playing cards. What is the probability that a card picked at rando

ale4655 [162]

Answer:

16/52, or 4/13.

Step-by-step explanation:

First, since we know that the question is asking for the probability of a club <u>or</u> a jack, we know that we have to add the two probabilities. The first probability is that of picking a club, which is 13/52. The probability of picking a jack (be sure not to overlap; don't double count the jack of clubs) is 3/52. Adding these two gives us 13/52+3/52=16/52, which simplifies to 4/13.

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3 years ago

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Rina8888 [55]

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3 years ago