1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Sav [38]
3 years ago
15

Solve for x.

Mathematics
2 answers:
Kruka [31]3 years ago
6 0

<u>Answer:</u>

x = \frac{2}{3} + \frac{\sqrt{10} }{3} , x = \frac{2}{3} - \frac{\sqrt{10} }{3}

<u>Step-by-step explanation:</u>

Multiplying the coefficient of x by the constant to get:

3 x (-2) = -6

Find factors of -6 that equal the middle term -4.

Since, no such factors can be found so we can solve the equation by completing the square.

To complete the square, divide the equation by the coefficient of x^2 which is 3 to get:

x^{2} - \frac{4}{3} x - \frac{2}{3} = 0

x^{2} - \frac{4}{3} x = \frac{2}{3}

Now divide the coefficient of x by 2 and add the square of the result to both sides of the equation:

x^{2} - \frac{4}{3} x + (-\frac{2}{3} )^{2} = \frac{2}{3} +  (-\frac{2}{3} )^{2}

(x - \frac{2}{3} )^2 = \frac{2}{3} + \frac{4}{9}

(x - \frac{2}{3} )^2 = \frac{4}{9}

\sqrt{(x - \frac{2}{3} )^2} = \sqrt{\frac{4}{9} }

x - \frac{2}{3} = \sqrt{\frac{10}{9} } , x - \frac{2}{3} = -\sqrt{\frac{10}{9} }

x = \frac{2}{3} + \frac{\sqrt{10} }{3} , x = \frac{2}{3} - \frac{\sqrt{10} }{3}



Ivahew [28]3 years ago
3 0
ANSWER

x=\frac{2-\sqrt{10}} {3}

or

x=\frac{\sqrt{10}+2} {3}

We have

3x^2-4x-2=0

Since we cannot factor easily, we complete the square.

Adding 2 to both sides give,

3x^2-4x=2

Dividing through by 3 gives

x^2-\frac{4}{3}x= \frac{2}{3}

Adding (-\frac{2}{3})^2 to both sides gives

x^2-\frac{4}{3}x+(-\frac{2}{3})^2= \frac{2}{3}+(-\frac{2}{3})^2

The expression on the Left Hand side is a perfect square.

(x-\frac{2}{3})^2= \frac{2}{3}+\frac{4}{9}

\Rightarrow (x-\frac{2}{3})^2= \frac{10}{9}

\Rightarrow (x-\frac{2}{3})=\pm \sqrt{\frac{10}{9}}

\Rightarrow (x)=\frac{2}{3} \pm {\frac{\sqrt{10}}{3}

Splitting the plus or minus sign gives

x=\frac{2- \sqrt{10}} {3}

or

x=\frac{\sqrt{10}+2} {3}
You might be interested in
Shape 1 and shape 2 are plotted on a coordinate plane. Which rigid transformation can you perform on shape 2 to show that shape
Aleksandr-060686 [28]
The answer is B. Take the same point on each of the figures and count how far they are away horizontally and vertically.
5 0
3 years ago
Blair is ordering 150 t-shirt to sell at the school carnival
Hatshy [7]
Then he should sell all of them for 3 dollars and he'll get $450 dollars from all 150 t-shirts
6 0
3 years ago
Add 4xly, -2xy?, -5xy?, 312y​ <br>step by step explanation plzz
storchak [24]

Answer:

8xy that is the answer...................

8 0
3 years ago
This is Grade 9 Mathematics so I kinda stuck here so, if somebody can help me Please sin30⁰+csc60⁰​
mamaluj [8]

\huge\mathrm{Answer࿐}

  • \sin(30)  +  \csc(60)

  • \dfrac{1}{2}  +  \dfrac{2}{ \sqrt{3} }

  • \dfrac{ \sqrt{3 } + 4 }{2 \sqrt{3} }

To remove √3 from denominator, we multiply both numerator as well as denominator with √3

  • \dfrac{ \sqrt{3 } + 4 }{2 \sqrt{3} }  \times  \dfrac{ \sqrt{3} }{ \sqrt{3} }

  • \dfrac{3 + 4 \sqrt{3} }{6}

____________________________

\mathrm{ \#TeeNForeveR}

6 0
3 years ago
Read 2 more answers
Write and solve the equation and then check your answer.
sweet-ann [11.9K]

Answer:

- The correct equation is 6s = 7.80

- The solution of the equation is s = $1.30

Step-by-step explanation:

To find the product of 6 and a number, first we denote the unknown number as s.

The product of 6 and s is the same as 6s.

If the product of both numbers is $7.80, then 6s = $7.80

The correct equation is therefore 6s = $7.80

To get the value of s, we will divide both sides by 6 to have:

6s/6 = $7.80/6

s = $1.30

Based on the calculation, the following statements are true

- The correct equation is 6s = 7.80

- The solution of the equation is s = $1.30

8 0
3 years ago
Read 2 more answers
Other questions:
  • I need both of these equations to be functioned into general form:
    12·1 answer
  • Laila read 36 pages in 4 hours. Which expression can be used to find the number of pages she read per hour?
    11·2 answers
  • Dawn has 12 yards of silk. She needs 1 1/4 yards of silk to make one skirt. How many skirts can she make?
    5·2 answers
  • What is the cube root of b^27
    8·1 answer
  • Describe a real world situation that would show a strong negative correlation explain your reasoning
    7·1 answer
  • 12,108 round to nearest thousand
    7·1 answer
  • 1)The recipe for a tall (12
    12·1 answer
  • I don't have a question this thing will not let me erase :)
    12·2 answers
  • The parallelogram is dilated by a scale factor of
    10·1 answer
  • 1. A(–6 , 2) , B(4 ,7) are endpoints of a line segment.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!