Solve 96*20=(2-6-2x)(20-x)

$$96 \times 20 = ( 2 - 6 - 2 x ) ( 20 - x )$$

Solve for x

$$x=\sqrt{1081}+9\approx 41.878564446$$

$$x=9-\sqrt{1081}\approx -23.878564446$$

Steps Using the Quadratic Formula

Multiply 96 and 20 to get 1920.

$$1920=\left(2-6-2x\right)\left(20-x\right)$$

Subtract 6 from 2 to get -4.

$$1920=\left(-4-2x\right)\left(20-x\right)$$

Use the distributive property to multiply -4-2x by 20-x and combine like terms.

$$1920=-80-36x+2x^{2}$$

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

$$-80-36x+2x^{2}=1920$$

Subtract 1920 from both sides.

$$-80-36x+2x^{2}-1920=0$$

Subtract 1920 from -80 to get -2000.

$$-2000-36x+2x^{2}=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$2x^{2}-36x-2000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, -36 for b, and -2000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-36\right)±\sqrt{\left(-36\right)^{2}-4\times 2\left(-2000\right)}}{2\times 2}$$

Square -36.

$$x=\frac{-\left(-36\right)±\sqrt{1296-4\times 2\left(-2000\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-\left(-36\right)±\sqrt{1296-8\left(-2000\right)}}{2\times 2}$$

Multiply -8 times -2000.

$$x=\frac{-\left(-36\right)±\sqrt{1296+16000}}{2\times 2}$$

Add 1296 to 16000.

$$x=\frac{-\left(-36\right)±\sqrt{17296}}{2\times 2}$$

Take the square root of 17296.

$$x=\frac{-\left(-36\right)±4\sqrt{1081}}{2\times 2}$$

The opposite of -36 is 36.

$$x=\frac{36±4\sqrt{1081}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{36±4\sqrt{1081}}{4}$$

Now solve the equation x=\frac{36±4\sqrt{1081}}{4} when ± is plus. Add 36 to 4\sqrt{1081}.

$$x=\frac{4\sqrt{1081}+36}{4}$$

Divide 36+4\sqrt{1081} by 4.

$$x=\sqrt{1081}+9$$

Now solve the equation x=\frac{36±4\sqrt{1081}}{4} when ± is minus. Subtract 4\sqrt{1081} from 36.

$$x=\frac{36-4\sqrt{1081}}{4}$$

Divide 36-4\sqrt{1081} by 4.

$$x=9-\sqrt{1081}$$

The equation is now solved.

$$x=\sqrt{1081}+9 x=9-\sqrt{1081}$$

Steps for Completing the Square

Multiply 96 and 20 to get 1920.

$$1920=\left(2-6-2x\right)\left(20-x\right)$$

Subtract 6 from 2 to get -4.

$$1920=\left(-4-2x\right)\left(20-x\right)$$

Use the distributive property to multiply -4-2x by 20-x and combine like terms.

$$1920=-80-36x+2x^{2}$$

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

$$-80-36x+2x^{2}=1920$$

Add 80 to both sides.

$$-36x+2x^{2}=1920+80$$

Add 1920 and 80 to get 2000.

$$-36x+2x^{2}=2000$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$2x^{2}-36x=2000$$

Divide both sides by 2.

$$\frac{2x^{2}-36x}{2}=\frac{2000}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x^{2}+\left(-\frac{36}{2}\right)x=\frac{2000}{2}$$

Divide -36 by 2.

$$x^{2}-18x=\frac{2000}{2}$$

Divide 2000 by 2.

$$x^{2}-18x=1000$$

Divide -18, the coefficient of the x term, by 2 to get -9. Then add the square of -9 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-18x+\left(-9\right)^{2}=1000+\left(-9\right)^{2}$$

Square -9.

$$x^{2}-18x+81=1000+81$$

Add 1000 to 81.

$$x^{2}-18x+81=1081$$

Factor x^{2}-18x+81. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-9\right)^{2}=1081$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-9\right)^{2}}=\sqrt{1081}$$

Simplify.

$$x-9=\sqrt{1081} x-9=-\sqrt{1081}$$

Add 9 to both sides of the equation.

$$x=\sqrt{1081}+9 x=9-\sqrt{1081}$$