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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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DochEvi [55]
The answer is B.

I hope this helps!
7 0
3 years ago
Simplify to create an equivalent expression. 8−4(−x+5)
White raven [17]
8 - 4(-x + 5)

As you already know, in order to find the equivalent expression to our already given one, we have to simplify it first :)

8 +4x - 20

**Remember that a negative times a negative is always a positive!!**

Add like terms.

4x + (8 - 20)

Simplify.

4x + (-12)

Get rid of parenthesis.

4x - 12

Look at our answer choices.

Our answer is a. 4x - 12

~Hope I helped!~
3 0
3 years ago
Angela invested $4000 in an account that earns 5% interest yearly (simple interest). She forgets about it for 12 years. What is
harina [27]

Answer:

$6400

Step-by-step explanation:

4000x.05=200× 12=2400+4000=$6400

4 0
3 years ago
Foram prescritos 500mg de dipirona para uma criança com febre.Na unidade tem disponivel ampola de 1g/2ml.Quantos g vão ser admin
Valentin [98]

De acordo com a disponibilidade da unidade, há apenas a seguinte dosagem: 1g/2mL - ou seja, uma grama de dipirona a cada 2mL

O enunciado está meio mal formulado, pois é dito que foram prescritos 500mg de dipirona e é essa quantidade de farmaco que a criança tem que tomar. Deseja-se saber quantos mL deverao ser administrados.

Fazendo a classica regra de 3, podemos chegar no volume desejado:

(atentar que 500mg = 0,5g)

     g               mL

     1    ---------   2

    0,5  ---------  X    

1 . X = 0,5 . 2

<h3>X = 1mL</h3>

8 0
3 years ago
What is the distance between (5, -1) and (5,-4)<br><br> 1 unit<br> 3 unit<br> 4 unit<br> 5 unit
Anton [14]

Answer:

3 units  

Step-by-step explanation:

8 0
2 years ago
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