Question

Solve for x
$3{x}^{2} - 6x + 2 = 0$
​

Answer 1

Answer:

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

Step-by-step explanation:

Mark as Brainlies

Answer 2

Answer:

$\Large\boxed{x=\frac{3+\sqrt{3}}{3}, \quad x=\frac{3-\sqrt{3}}{3}\quad X=1.57 \quad X=0.42}}}$

Step-by-step explanation:

Given:

To solve this problem, first you have to find the value of x from left to right. Isolate by the x on one side of the equation.

Solutions:

First, used quadratic equation formula.

$\Large\boxed{\textnormal{QUADRATIC EQUATION FORMULA}}$

$\displaystyle \frac{-B\pm\sqrt{B^2-4AC} }{2A}$

A=3

B=(-6)

C=2

$\displaystyle \frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:3\cdot \:2}}{2\cdot \:3}$

Solve.

$\Large\boxed{\textnormal{APPLY RULE}}$

$\displaystyle -(-Y)=Y$

$\displaystyle \frac{6+\sqrt{(-6)^2-4*3*2} }{2*3}$

$\displaystyle 6+\sqrt{(-6)^2-4*3*2 \quad =6+\sqrt{12}$

$\displaystyle \frac{6+\sqrt{12} }{2*3}$

Next, multiply the numbers from left to right.

$\displaystyle 3*2=6$

$\displaystyle \frac{6+\sqrt{12} }{6}$

$\displaystyle 2\sqrt{3}=\sqrt{12}$

$\displaystyle\frac{6+2\sqrt{3}}{6}$

Factor it out.

$\displaystyle \frac{6+2\sqrt{3}}{6}=2(3+\sqrt{3})$

$\displaystyle\frac{2\left(3+\sqrt{3}\right)}{6}$

Common factor of 2.

$\displaystyle \frac{3+\sqrt{3}}{3}$

Solve.

$\displaystyle\frac{-\left(-6\right)-\sqrt{\left(-6\right)^2-4* \:3* \:2}}{2\cdot \:3}=\Large\boxed{\frac{3-\sqrt{3}}{3}, \quad =\frac{3+\sqrt{3}}{3} }$

Therefore, the correct answer is x=3+√3/3, x=3-√3/3, x=1.57, and x=0.42.