Solve (20-2x)*(12-2x)=180

$$(20-2x) \times (12-2x)=180$$

Solve for x

$$x=15$$

$$x=1$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 20-2x by 12-2x and combine like terms.

$$240-64x+4x^{2}=180$$

Subtract 180 from both sides.

$$240-64x+4x^{2}-180=0$$

Subtract 180 from 240 to get 60.

$$60-64x+4x^{2}=0$$

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.

$$4x^{2}-64x+60=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, -64 for b, and 60 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-64\right)±\sqrt{\left(-64\right)^{2}-4\times 4\times 60}}{2\times 4}$$

Square -64.

$$x=\frac{-\left(-64\right)±\sqrt{4096-4\times 4\times 60}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{-\left(-64\right)±\sqrt{4096-16\times 60}}{2\times 4}$$

Multiply -16 times 60.

$$x=\frac{-\left(-64\right)±\sqrt{4096-960}}{2\times 4}$$

Add 4096 to -960.

$$x=\frac{-\left(-64\right)±\sqrt{3136}}{2\times 4}$$

Take the square root of 3136.

$$x=\frac{-\left(-64\right)±56}{2\times 4}$$

The opposite of -64 is 64.

$$x=\frac{64±56}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{64±56}{8}$$

Now solve the equation x=\frac{64±56}{8} when ± is plus. Add 64 to 56.

$$x=\frac{120}{8}$$

Divide 120 by 8.

$$x=15$$

Now solve the equation x=\frac{64±56}{8} when ± is minus. Subtract 56 from 64.

$$x=\frac{8}{8}$$

Divide 8 by 8.

$$x=1$$

The equation is now solved.

$$x=15 x=1$$

Steps for Completing the Square

Use the distributive property to multiply 20-2x by 12-2x and combine like terms.

$$240-64x+4x^{2}=180$$

Subtract 240 from both sides.

$$-64x+4x^{2}=180-240$$

Subtract 240 from 180 to get -60.

$$-64x+4x^{2}=-60$$

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.

$$4x^{2}-64x=-60$$

Divide both sides by 4.

$$\frac{4x^{2}-64x}{4}=-\frac{60}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x^{2}+\left(-\frac{64}{4}\right)x=-\frac{60}{4}$$

Divide -64 by 4.

$$x^{2}-16x=-\frac{60}{4}$$

Divide -60 by 4.

$$x^{2}-16x=-15$$

Divide -16, the coefficient of the x term, by 2 to get -8. Then add the square of -8 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-16x+\left(-8\right)^{2}=-15+\left(-8\right)^{2}$$

Square -8.

$$x^{2}-16x+64=-15+64$$

Add -15 to 64.

$$x^{2}-16x+64=49$$

Factor x^{2}-16x+64. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-8\right)^{2}=49$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-8\right)^{2}}=\sqrt{49}$$

Simplify.

$$x-8=7 x-8=-7$$

Add 8 to both sides of the equation.

$$x=15 x=1$$