Question

Solve 3x² + 4x = 2. (2 points)

Answer 1

Answer:

Step-by-step explanation:

As it is a second order equation, it means that it has two possible answers and they are $x_1$ and $x_2$.

The famous quadratic formula for solving any second order equation is the following:

$x_{1} = \frac{-b + \sqrt{b^2 - 4 ac}}{2a}\\x_{2}=\frac{-b - \sqrt{b^2 - 4 ac}}{2a}$

Where a is the coefficient of $x^2$, b is the coefficient of x, and c is the free term. In other words,

$a = 3\\b=4\\c=-2$

as the equation should be in the following form:

$a x^2 + bx+c = 0$

Therefore the possible answer should be the following,

$\frac{-4 + \sqrt{4^2 - 4*3*(-2)}}{2*3}=\frac{-4 +\sqrt{16 + 24}}{6} =\frac{-4 + \sqrt{40}}{6}=\\ \frac{-4 + \sqrt{4*10}}{6} = \frac{-4 + 2\sqrt{10}}{6}$$\frac{2*(-2 + \sqrt{10})}{2*3} = \frac{-2 + \sqrt{10}}{3}$

by dividing the numerator and denominator by 2, we can deduce the following,