Question

I need help with this and can I see the steps also?

Answer 1

Answer:

Nico is incorrect because he added 3x instead of subtracting 3x from both sides.

$x=-\frac{1+i\sqrt{23} }{2} , -\frac{1-i\sqrt{23} }{2}$

Step-by-step explanation:

Ok, so first we need to get the equation set to 0 so we have a quadratic equation.

$4x+6=3x-x^{2} \\x^{2} +4x+6=3x\\x^{2}+x+6=0$

Here you would begin to factor but this is not possible with this equation. There is not a solution set that would be a product of 6 and a sum of 1. So you have to use the quadratic formula.

$\frac{-b\pm \sqrt{b^{2}-4ac } }{2a}$

So if we look at our quadratic,

$(1)x^{2}+(1)x+6=0$

$ax^{2} +bx+c=0$

we know,

$a=1\\b=1\\c=6$

Now it's time to plug and play.

$\frac{-(1)\pm \sqrt{(1)^{2}-4(1)(6) } }{2(1)}\\\frac{-1\pm \sqrt{1-24 } }{2}\\\frac{-1\pm \sqrt{-23 } }{2}$

Ok, so it is impossible to have a negative root which means we have a complex number or imaginary number. We use $i$ to represent these imaginary numbers. We can't simplify the root anymore.

$\frac{-1\pm i\sqrt{23 } }{2}$