Question

HELP MEDAL AND FAN
2x^2+x=3-4x

Answer 1

hiya, r u ready for me to explain now colorfully

Answer 2

factor sorry

Answer 3

ya sure

Answer 4

First let's collect like terms to simplify things:

\[2x^2+x=3-4x\]\[2x^2+5x-3=0\]
Then use any method you like to solve for x (e.g. quadratic formula). You should get x = 0.5 and x = -3.

Answer 5

but you have to slove this by factoring

Answer 6

solve*

Answer 7

Equation to Solve
\(\color{red}{2*x^2+x=3−4*x}\)
Solution Steps
1. Negate
\(\color{purple}{2*x^2+x=3−4*x}\)
2. Multiply Terms
\(\color{blue}{2x^2+x=3−4x}\)
3. Order Terms
\(\color{gray}{2x^2+x=-4x+3}\)
4. Move Variables to Left
\(\color{lightblue}{2x2+x+4x=3}\)
5. Add Terms
\(\color{green}{2x^2+5x=3}\)
6. Factor Trinomial
\(\color{darkgreen}{(x+3)*(2x−1)=0}\)
Forked Equation 1
\(\color{violet}{x+3=0}\)
Forked Equation 2
2x−1=0
Now Solving Equation 1
\(\color{yellow}{x+3=0}\)
7. Move Constants to Right
x=0−3
8. Remove Zero Terms
x=-3
End of Equation 1
Now Solving Equation 2
2x−1=0
9. Move Constants to Right
2x=0+1
10. Remove Zero Terms
2x=1
11. Divide Both Sides by Term
x=12
End of Equation 2
Plug candidate answers into original equation...
Answer 1:
-3
Answer 2:
12

Answer 8

No problem! I'm going to start with my second equation up there:

\[2x^2+5x-3=0\]
To factor this, we need to find two numbers that add to give 5 and multiply to give -6 (which you get from 2 * -3). The only two numbers are -1 and 6. We can then rewrite the middle term, 5x, as 6x - x since they're equal:

\[2x^2+6x-x-3=0\]
Next we need to group the terms in a way that let's us factor them more easily. We can do it like this:

\[(2x^2-x)+(6x-3)=0\]
I just switched the positions of 6x and -x, and drew brackets around the groups that can now be factored. Now we can finish!

\[x(2x-1)+3(2x-1)=0\]\[(2x-1)(x+3)=0\]\[x=\frac{ 1 }{ 2 },-3\]

Answer 9

yes 1/2 sorry typo