Solve left(2x-8right)left(x-6right)=2

$$\left( 2x-8 \right) \left( x-6 \right) = 2$$

Solve for x

$$x=\sqrt{2}+5\approx 6.414213562$$

$$x=5-\sqrt{2}\approx 3.585786438$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2x-8 by x-6 and combine like terms.

$$2x^{2}-20x+48=2$$

Subtract 2 from both sides.

$$2x^{2}-20x+48-2=0$$

Subtract 2 from 48 to get 46.

$$2x^{2}-20x+46=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, -20 for b, and 46 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}-4\times 2\times 46}}{2\times 2}$$

Square -20.

$$x=\frac{-\left(-20\right)±\sqrt{400-4\times 2\times 46}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-\left(-20\right)±\sqrt{400-8\times 46}}{2\times 2}$$

Multiply -8 times 46.

$$x=\frac{-\left(-20\right)±\sqrt{400-368}}{2\times 2}$$

Add 400 to -368.

$$x=\frac{-\left(-20\right)±\sqrt{32}}{2\times 2}$$

Take the square root of 32.

$$x=\frac{-\left(-20\right)±4\sqrt{2}}{2\times 2}$$

The opposite of -20 is 20.

$$x=\frac{20±4\sqrt{2}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{20±4\sqrt{2}}{4}$$

Now solve the equation x=\frac{20±4\sqrt{2}}{4} when ± is plus. Add 20 to 4\sqrt{2}.

$$x=\frac{4\sqrt{2}+20}{4}$$

Divide 20+4\sqrt{2} by 4.

$$x=\sqrt{2}+5$$

Now solve the equation x=\frac{20±4\sqrt{2}}{4} when ± is minus. Subtract 4\sqrt{2} from 20.

$$x=\frac{20-4\sqrt{2}}{4}$$

Divide 20-4\sqrt{2} by 4.

$$x=5-\sqrt{2}$$

The equation is now solved.

$$x=\sqrt{2}+5 x=5-\sqrt{2}$$

Steps for Completing the Square

Use the distributive property to multiply 2x-8 by x-6 and combine like terms.

$$2x^{2}-20x+48=2$$

Subtract 48 from both sides.

$$2x^{2}-20x=2-48$$

Subtract 48 from 2 to get -46.

$$2x^{2}-20x=-46$$

Divide both sides by 2.

$$\frac{2x^{2}-20x}{2}=-\frac{46}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x^{2}+\left(-\frac{20}{2}\right)x=-\frac{46}{2}$$

Divide -20 by 2.

$$x^{2}-10x=-\frac{46}{2}$$

Divide -46 by 2.

$$x^{2}-10x=-23$$

Divide -10, the coefficient of the x term, by 2 to get -5. Then add the square of -5 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-10x+\left(-5\right)^{2}=-23+\left(-5\right)^{2}$$

Square -5.

$$x^{2}-10x+25=-23+25$$

Add -23 to 25.

$$x^{2}-10x+25=2$$

Factor x^{2}-10x+25. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-5\right)^{2}=2$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-5\right)^{2}}=\sqrt{2}$$

Simplify.

$$x-5=\sqrt{2} x-5=-\sqrt{2}$$

Add 5 to both sides of the equation.

$$x=\sqrt{2}+5 x=5-\sqrt{2}$$