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ryzh [129]
2 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]2 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]2 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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