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ryzh [129]
3 years ago
9

Solve 3x2 + 4x = 2. TEACH me how to solve this.. I know what to do once I have it in the right forum... but I do not understand

how to simplify it down.
a. quantity of 2 plus or minus square root of 10 all over 6
b. quantity of negative 2 plus or minus 2 square root of 10 all over 3
c. quantity of negative 2 plus or minus square root of 10 all over 3
d. quantity of 4 plus or minus square root of 10 all over 3
Mathematics
2 answers:
pentagon [3]3 years ago
8 0
Here is our quadratic:
3x^2+4x=2

There are three different methods we can use. I'll explain each in depth.

Factoring
If you want to factor, bring everything over to the left side like so:
<em>3x² + 4x = 2 </em><em>| subtract 2 from each side
</em>3x² + 4x - 2 = 0
Now, we need to find two numbers that add to our x coefficient 4 and multiply to make -6. (our x² coefficient times our constant) There's no whole number answer to that, so factoring isn't going to work.
<em>If we had something like 2x² + 13x + 15 = 0, here's how we'd factor:
</em><em>We want two numbers that add to 13 and multiply to 30...these would be 10 and 3.
</em><em>Now we "split the middle" into these numbers.
</em><em>2x² + 10x + 3x + 15 = 0
</em><em>Factor the first two and last two terms. You should get the same thing inside the parentheses of each.
</em><em>2x(x+5) + 3(x+5) = 0
</em><em>(2x+3)(x+5) = 0
</em><em>Any value of x which causes a factor to equal zero would be a solution.
</em><em>2x + 3 = 0  </em>⇒ <em>2x = -3 </em>⇒ <em>x = -3/2
</em><em>x + 5 = 0 </em>⇒ <em>x = -5
</em>
Completing the square
For this one, keep the constant on the right side.
<em>3x² + 4x = 2</em>
Our x² coefficient needs to be 1, so let's divide by 3.
<em>x² + 4/3x = 2/3
</em>Now we take our x coefficient, halve it, square it, and add it to each side.
<em>Half of 4/3 is 2/3, square that to get 4/9...
</em><em>x² + 4/3x + 4/9 = 2/3 + 4/9
</em><em>x² + 4/3x + 4/9 = 10/9
</em><em />Factor the perfect square trinomial on the left.
(Because we set this up as a perfect square trinomial, just halve the x coefficient and add that to x. Square it for your factored form.)
<em>(x+2/3)² = 10/9 | Take the square root of each side
x+2/3 = </em>±√<em>(10/9)
x+2/3 = </em>±√<em>(10)/3 | Subtract 2/3 from each side.
x = </em>±√<em>(10)/3-2/3
</em>Under one denominator...
x = (-2±√<em />10)/3 (answer C)
<em>
</em>Using the quadratic formula
<em />The solution to any quadratic ax^2+bx+c=0 is x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.
In the case of our quadratic 3x² + 4x - 2 = 0...
a = 3, b = 4, and c = -2.
Plug these into our formula and simplify.
x=\frac{-4\pm\sqrt{4^2-4(3)(-2)}}{2(3)}=\frac{-4\pm\sqrt{16+24}}{6}=\frac{-4\pm\sqrt{40}}{6}=\frac{-4\pm2\sqrt{10}}{6}=\boxed{\frac{-2\pm\sqrt{10}}{3}}
sertanlavr [38]3 years ago
7 0
So if it is 3x^2+4x=2 then
set one side to zero
subtract 2 from both sides
3x^2+4x-2=0
this is not factorable by normal means so use quadratic formula which is if you have the equation in ax^2+bx+c=0 form you can solve for x if you put it into this equation quadratic formula x=\frac{-b+ \sqrt{b^2-4ac} }{2a} or  \frac{-b- \sqrt{b^2-4ac} }{2a} so if you were to input it into this equation you would get
a=3
b=4
c=-2

the solution is x= \frac{-2+ \sqrt{10} }{3} or \frac{-2- \sqrt{10} }{3}
the answer is  C
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Elden [556K]

Answer:

x = 2/5

General Formulas and Concepts:

Order of Operations: BPEMDAS

Step-by-step explanation:

<u>Step 1: Write equation</u>

5x = 2

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Divide both sides by 5:          x = 2/5

<u>Step 3: Check</u>

<em>Plug in x to verify it's a solution</em>.

  1. Substitute:                    5(2/5) = 2
  2. Multiply:                        10/5 = 2
  3. Divide:                           2 = 2
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3 years ago
What is the distance between parallel lines y=x+3 and y=x+1, rounded to the nearest hundredth?
riadik2000 [5.3K]

Answer:

The distance is 1.41 to nearest hundredth.

Step-by-step explanation:

The line y = x + 3 passes through the point (0, 3) on the yaxis.

Find the perpendicular line passing through this point:

y  - 3 = -1(x + 0)

y = -x + 3

Now find the point where this line intersects the line y = x + 1:

y = -x + 3

y = x + 1

-x + 3 = x  + 1

3 -1 = x + x

2x = 2

x = 1

and y = 2

So this point is (1, 2)

We require the distance between this point and (0, 3)

This = √((3-2)^2 + (0-1)^2) = √2

= 1.4142

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2 years ago
How many times does blood culirculate in an hour
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Your blood circulates a total of 128 times a hour, or 3 times a minute.
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@FauxGeoDuck
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Alexus is ordering a large pizza for lunch. She has $15 dollars in all. A large pizza costs $9 and
exis [7]

Step-by-step explanation:

It would be

9+6 because 0.50 is a dollar so if u multiply by 6 and add the 9 the equation would be 9+6.......

don't forget get to rate me thx:)

4 0
3 years ago
The expression p/x^2 - 5x +6 simplifies to x+4/x-2. Which expression doees p represent?
gladu [14]
We know that
(ad)/(bd)=d/d time a/b=a/b since d's cancel
also
if a/b=c/d in simplest form, then a=c and b=d

we have
p/(x^2-5x+6)=(x+4)/(x-2)
therefor

p/(x^2-5x+6)=d/d times (x+4)/(x-2)
p/(x^2-5x+6)=d(x+4)/d(x-2)

therefor
p=d(x+4) and
x^2-5x+6=d(x-2)

we can solve last one
factor
(x-6)(x+1)=d(x-2)
divide both sides by (x-2)
[(x-6)(x+1)]/(x-2)=d
sub


p=d(x+4)
p=([(x-6)(x+1)]/(x-2))(x+4)
p= \frac {(x-6)(x+1)(x+4)}{(x-2)}

7 0
3 years ago
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