Question

Solve:$3x^2-2x=-1$

Short answer

The value of$x=1\pm i\sqrt{2}$

Step-by-step solution

Step 1. Given information.

Quadratic equation is:

$3x^2-2x=-1$

We can rewrite the equation as:

$3x^2-2x+1=0$

Step 2. Find solution of x.

By comparing $3x^2-2x+1=0$, with standard quadratic equation: $a{x}^2+bx+c=0$.

We get,

$$\begin{gathered} a=3 \\ b=-2 \\ c=1 \end{gathered}$$

Substitute these values in the formula and solve.

$$\begin{gathered} x=\frac{-(-2)\pm \sqrt{{(-2)}^2-4\left(3\right)\left(1\right)}}{2\left(1\right)} \\ x=\frac{2\pm \sqrt{4-12}}{2} \\ x=\frac{2\pm \sqrt{-8}}{2} \\ x=\frac{2\pm \sqrt{8i^2}}{2} \\ x=\frac{2\pm i2\sqrt{2}}{2} \\ x=\frac{2(1\pm i\sqrt{2})}{2} \\ x=1\pm i\sqrt{2} \end{gathered}$$