Solve Using the Quadratic Formula 3x^2-6x+1=0

Problem

$3x^2-6x+1=0$

Solution

1. Identify the coefficients $a$ $b$ and $c$ from the standard form $a{x}^2+bx+c=0$

$a=3$

$b=-6$

$c=1$

2. State the quadratic formula.

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

3. Substitute the values of $a$ $b$ and $c$ into the formula.

$x=\frac{-(-6)\pm \sqrt{{(-6)}^2-4\left(3\right)\left(1\right)}}{2\left(3\right)}$

4. Simplify the expression under the square root (the discriminant).

$x=\frac{6\pm \sqrt{36-12}}{6}$

$x=\frac{6\pm \sqrt{24}}{6}$

5. Simplify the radical by factoring out the largest perfect square.

$x=\frac{6\pm \sqrt{4\cdot 6}}{6}$

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

6. Divide each term in the numerator by the denominator to find the final simplified values.

$x=\frac{2(3\pm \sqrt{6})}{6}$

$x=\frac{3\pm \sqrt{6}}{3}$

Final Answer

$x=\frac{3\pm \sqrt{6}}{3}$

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