Solve for x. 3x^2-4x-2=0

Enter your simplified answers, as exact values, in the boxes

Answers

Answer 1

Answer: ANSWER

$x=\frac{2-√(10)} {3}$

or

$x=\frac{√(10)+2} {3}$

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

$x^2-(4)/(3)x= (2)/(3)$

Adding $(-(2)/(3))^2$ to both sides gives

$x^2-(4)/(3)x+(-(2)/(3))^2= (2)/(3)+(-(2)/(3))^2$

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

$(x-(2)/(3))^2= (2)/(3)+(4)/(9)$

$\Rightarrow (x-(2)/(3))^2= (10)/(9)$

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

$\Rightarrow (x)=(2)/(3) \pm {(√(10))/(3)$

Splitting the plus or minus sign gives

$x=\frac{2- √(10)} {3}$

or

$x=\frac{√(10)+2} {3}$

Answer 2

Answer:

Answer:

$x = (2)/(3) + (√(10) )/(3) , x = (2)/(3) - (√(10) )/(3)$

Step-by-step explanation:

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:

$x^(2) - (4)/(3) x - (2)/(3) = 0$

$x^(2) - (4)/(3) x = (2)/(3)$

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

$x^(2) - (4)/(3) x + (-(2)/(3) )^(2) = (2)/(3) + (-(2)/(3) )^(2)$

$(x - (2)/(3) )^2 = (2)/(3) + (4)/(9)$

$(x - (2)/(3) )^2 = (4)/(9)$

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

$x - (2)/(3) = \sqrt{(10)/(9) }$ , $x - (2)/(3) = -\sqrt{(10)/(9) }$

$x = (2)/(3) + (√(10) )/(3) , x = (2)/(3) - (√(10) )/(3)$

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What is the greatest common factor of the pair of numbers?104 and 260

Question 9 options:

4

13

20

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Answers

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the greatest common factor of 104 and 260 is 52

Simplify the polynomial (3a^2+4a+25) - (2a^2+4a-5)

Answers

Answer:

The polynomial simplified would be a^2 + 30

I hope this helps you:))

P.S. Might I recommend a good online calculator for these types of problems. It's called Symbolab. I use it every day and it's a lifesaver. It shows the step-by-step and has a plethora of different actions like simplifying, inverse, and line.

-3(x + 4) = (-x - 1)

Answers

Answer:

x=-5.5

Step-by-step explanation:

-3(x+4)=(-x-1)

1. Distribute

-3x+(-12)=-x-1

2. Simplify

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-2x=11

x=-11/2

x=-5.5

Answer:

-11/2 or 5.5

Step-by-step explanation:

A car depreciated $1500 each year it was owned and driven. What type of depreciation is this?

Answers

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If the function f(x) = mx + b has an inverse function, which statement must be true?

Answers

f(x) = mx + b is just equal to the equation
y = mx + b

In order for us to get the inverse function, then we can interchange x to y and y to x
y = mx + b
x = my + b

Then we need to find y
x = my + b
-my = -x + b
my = x - b
y = (x-b) / m
f(x) = (x - b) / m

Answer:

m ≠ 0

Step-by-step explanation:

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