Solve 0=x^2-8x-2

$$0 = { x }^{ 2 } -8x-2$$

Solve for x

$$x=3\sqrt{2}+4\approx 8.242640687$$

$$x=4-3\sqrt{2}\approx -0.242640687$$

Steps Using the Quadratic Formula

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

$$x^{2}-8x-2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -8 for b, and -2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\left(-2\right)}}{2}$$

Square -8.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\left(-2\right)}}{2}$$

Multiply -4 times -2.

$$x=\frac{-\left(-8\right)±\sqrt{64+8}}{2}$$

Add 64 to 8.

$$x=\frac{-\left(-8\right)±\sqrt{72}}{2}$$

Take the square root of 72.

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

The opposite of -8 is 8.

$$x=\frac{8±6\sqrt{2}}{2}$$

Now solve the equation x=\frac{8±6\sqrt{2}}{2} when ± is plus. Add 8 to 6\sqrt{2}.

$$x=\frac{6\sqrt{2}+8}{2}$$

Divide 8+6\sqrt{2} by 2.

$$x=3\sqrt{2}+4$$

Now solve the equation x=\frac{8±6\sqrt{2}}{2} when ± is minus. Subtract 6\sqrt{2} from 8.

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

Divide 8-6\sqrt{2} by 2.

$$x=4-3\sqrt{2}$$

The equation is now solved.

$$x=3\sqrt{2}+4 x=4-3\sqrt{2}$$

Steps for Completing the Square

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

$$x^{2}-8x-2=0$$

Add 2 to both sides. Anything plus zero gives itself.

$$x^{2}-8x=2$$

Divide -8, the coefficient of the x term, by 2 to get -4. Then add the square of -4 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-8x+\left(-4\right)^{2}=2+\left(-4\right)^{2}$$

Square -4.

$$x^{2}-8x+16=2+16$$

Add 2 to 16.

$$x^{2}-8x+16=18$$

Factor x^{2}-8x+16. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-4\right)^{2}=18$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-4\right)^{2}}=\sqrt{18}$$

Simplify.

$$x-4=3\sqrt{2} x-4=-3\sqrt{2}$$

Add 4 to both sides of the equation.

$$x=3\sqrt{2}+4 x=4-3\sqrt{2}$$