Solve 0=x^2-6x+2

$$0 = x ^ { 2 } - 6 x + 2$$

Solve for x

$$x=\sqrt{7}+3\approx 5.645751311$$

$$x=3-\sqrt{7}\approx 0.354248689$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$x^{2}-6x+2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -6 for b, and 2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 2}}{2}$$

Square -6.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\times 2}}{2}$$

Multiply -4 times 2.

$$x=\frac{-\left(-6\right)±\sqrt{36-8}}{2}$$

Add 36 to -8.

$$x=\frac{-\left(-6\right)±\sqrt{28}}{2}$$

Take the square root of 28.

$$x=\frac{-\left(-6\right)±2\sqrt{7}}{2}$$

The opposite of -6 is 6.

$$x=\frac{6±2\sqrt{7}}{2}$$

Now solve the equation x=\frac{6±2\sqrt{7}}{2} when ± is plus. Add 6 to 2\sqrt{7}.

$$x=\frac{2\sqrt{7}+6}{2}$$

Divide 6+2\sqrt{7} by 2.

$$x=\sqrt{7}+3$$

Now solve the equation x=\frac{6±2\sqrt{7}}{2} when ± is minus. Subtract 2\sqrt{7} from 6.

$$x=\frac{6-2\sqrt{7}}{2}$$

Divide 6-2\sqrt{7} by 2.

$$x=3-\sqrt{7}$$

The equation is now solved.

$$x=\sqrt{7}+3 x=3-\sqrt{7}$$

Steps for Completing the Square

Swap sides so that all variable terms are on the left hand side.

$$x^{2}-6x+2=0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}-6x=-2$$

Divide -6, the coefficient of the x term, by 2 to get -3. Then add the square of -3 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-6x+\left(-3\right)^{2}=-2+\left(-3\right)^{2}$$

Square -3.

$$x^{2}-6x+9=-2+9$$

Add -2 to 9.

$$x^{2}-6x+9=7$$

Factor x^{2}-6x+9. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-3\right)^{2}=7$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{7}$$

Simplify.

$$x-3=\sqrt{7} x-3=-\sqrt{7}$$

Add 3 to both sides of the equation.

$$x=\sqrt{7}+3 x=3-\sqrt{7}$$