Solve 2x^2-8x-2*20=0

$$2 { x }^{ 2 } -8x-2 \times 20 = 0$$

Solve for x

$$x=2\sqrt{6}+2\approx 6.898979486$$

$$x=2-2\sqrt{6}\approx -2.898979486$$

Steps Using the Quadratic Formula

Multiply 2 and 20 to get 40.

$$2x^{2}-8x-40=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, -8 for b, and -40 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 2\left(-40\right)}}{2\times 2}$$

Square -8.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\times 2\left(-40\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-\left(-8\right)±\sqrt{64-8\left(-40\right)}}{2\times 2}$$

Multiply -8 times -40.

$$x=\frac{-\left(-8\right)±\sqrt{64+320}}{2\times 2}$$

Add 64 to 320.

$$x=\frac{-\left(-8\right)±\sqrt{384}}{2\times 2}$$

Take the square root of 384.

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

The opposite of -8 is 8.

$$x=\frac{8±8\sqrt{6}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{8±8\sqrt{6}}{4}$$

Now solve the equation x=\frac{8±8\sqrt{6}}{4} when ± is plus. Add 8 to 8\sqrt{6}.

$$x=\frac{8\sqrt{6}+8}{4}$$

Divide 8+8\sqrt{6} by 4.

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

Now solve the equation x=\frac{8±8\sqrt{6}}{4} when ± is minus. Subtract 8\sqrt{6} from 8.

$$x=\frac{8-8\sqrt{6}}{4}$$

Divide 8-8\sqrt{6} by 4.

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

The equation is now solved.

$$x=2\sqrt{6}+2 x=2-2\sqrt{6}$$

Steps for Completing the Square

Multiply 2 and 20 to get 40.

$$2x^{2}-8x-40=0$$

Add 40 to both sides. Anything plus zero gives itself.

$$2x^{2}-8x=40$$

Divide both sides by 2.

$$\frac{2x^{2}-8x}{2}=\frac{40}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x^{2}+\left(-\frac{8}{2}\right)x=\frac{40}{2}$$

Divide -8 by 2.

$$x^{2}-4x=\frac{40}{2}$$

Divide 40 by 2.

$$x^{2}-4x=20$$

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

$$x^{2}-4x+\left(-2\right)^{2}=20+\left(-2\right)^{2}$$

Square -2.

$$x^{2}-4x+4=20+4$$

Add 20 to 4.

$$x^{2}-4x+4=24$$

Factor x^{2}-4x+4. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-2\right)^{2}=24$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{24}$$

Simplify.

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

Add 2 to both sides of the equation.

$$x=2\sqrt{6}+2 x=2-2\sqrt{6}$$