# Evaluate: 3x^2-2x+1=0

## Expression: $3{x}^{2}-2x+1=0$

Identify the coefficients $a$, $b$ and $c$ of the quadratic equation

$\begin{array} { l }a=3,& b=-2,& c=1\end{array}$

Substitute $a=3$, $b=-2$ and $c=1$ into the quadratic formula $x=\frac{ -b\pm\sqrt{ {b}^{2}-4ac } }{ 2a }$

$x=\frac{ -\left( -2 \right)\pm\sqrt{ {\left( -2 \right)}^{2}-4 \times 3 \times 1 } }{ 2 \times 3 }$

Any expression multiplied by $1$ remains the same

$x=\frac{ -\left( -2 \right)\pm\sqrt{ {\left( -2 \right)}^{2}-4 \times 3 } }{ 2 \times 3 }$

When there is a $-$ in front of an expression in parentheses, change the sign of each term of the expression and remove the parentheses

$x=\frac{ 2\pm\sqrt{ {\left( -2 \right)}^{2}-4 \times 3 } }{ 2 \times 3 }$

Evaluate the power

$x=\frac{ 2\pm\sqrt{ 4-4 \times 3 } }{ 2 \times 3 }$

Multiply the numbers

$x=\frac{ 2\pm\sqrt{ 4-12 } }{ 2 \times 3 }$

Multiply the numbers

$x=\frac{ 2\pm\sqrt{ 4-12 } }{ 6 }$

Calculate the difference

$x=\frac{ 2\pm\sqrt{ -8 } }{ 6 }$

The square root of a negative number does not exist in the set of real numbers

$x\notin ℝ$

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