Solve (60-2x)(40-2x)=3/8*40*60

$$(60-2x)(40-2x)= \frac{ 3 }{ 8 } \times 40 \times 60$$

Solve for x

$$x=25-5\sqrt{10}\approx 9.188611699$$

$$x=5\sqrt{10}+25\approx 40.811388301$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 60-2x by 40-2x and combine like terms.

$$2400-200x+4x^{2}=\frac{3}{8}\times 40\times 60$$

Multiply \frac{3}{8} and 40 to get 15.

$$2400-200x+4x^{2}=15\times 60$$

Multiply 15 and 60 to get 900.

$$2400-200x+4x^{2}=900$$

Subtract 900 from both sides.

$$2400-200x+4x^{2}-900=0$$

Subtract 900 from 2400 to get 1500.

$$1500-200x+4x^{2}=0$$

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.

$$4x^{2}-200x+1500=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, -200 for b, and 1500 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-200\right)±\sqrt{\left(-200\right)^{2}-4\times 4\times 1500}}{2\times 4}$$

Square -200.

$$x=\frac{-\left(-200\right)±\sqrt{40000-4\times 4\times 1500}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{-\left(-200\right)±\sqrt{40000-16\times 1500}}{2\times 4}$$

Multiply -16 times 1500.

$$x=\frac{-\left(-200\right)±\sqrt{40000-24000}}{2\times 4}$$

Add 40000 to -24000.

$$x=\frac{-\left(-200\right)±\sqrt{16000}}{2\times 4}$$

Take the square root of 16000.

$$x=\frac{-\left(-200\right)±40\sqrt{10}}{2\times 4}$$

The opposite of -200 is 200.

$$x=\frac{200±40\sqrt{10}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{200±40\sqrt{10}}{8}$$

Now solve the equation x=\frac{200±40\sqrt{10}}{8} when ± is plus. Add 200 to 40\sqrt{10}.

$$x=\frac{40\sqrt{10}+200}{8}$$

Divide 200+40\sqrt{10} by 8.

$$x=5\sqrt{10}+25$$

Now solve the equation x=\frac{200±40\sqrt{10}}{8} when ± is minus. Subtract 40\sqrt{10} from 200.

$$x=\frac{200-40\sqrt{10}}{8}$$

Divide 200-40\sqrt{10} by 8.

$$x=25-5\sqrt{10}$$

The equation is now solved.

$$x=5\sqrt{10}+25 x=25-5\sqrt{10}$$

Steps for Completing the Square

Use the distributive property to multiply 60-2x by 40-2x and combine like terms.

$$2400-200x+4x^{2}=\frac{3}{8}\times 40\times 60$$

Multiply \frac{3}{8} and 40 to get 15.

$$2400-200x+4x^{2}=15\times 60$$

Multiply 15 and 60 to get 900.

$$2400-200x+4x^{2}=900$$

Subtract 2400 from both sides.

$$-200x+4x^{2}=900-2400$$

Subtract 2400 from 900 to get -1500.

$$-200x+4x^{2}=-1500$$

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.

$$4x^{2}-200x=-1500$$

Divide both sides by 4.

$$\frac{4x^{2}-200x}{4}=-\frac{1500}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x^{2}+\left(-\frac{200}{4}\right)x=-\frac{1500}{4}$$

Divide -200 by 4.

$$x^{2}-50x=-\frac{1500}{4}$$

Divide -1500 by 4.

$$x^{2}-50x=-375$$

Divide -50, the coefficient of the x term, by 2 to get -25. Then add the square of -25 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-50x+\left(-25\right)^{2}=-375+\left(-25\right)^{2}$$

Square -25.

$$x^{2}-50x+625=-375+625$$

Add -375 to 625.

$$x^{2}-50x+625=250$$

Factor x^{2}-50x+625. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-25\right)^{2}=250$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-25\right)^{2}}=\sqrt{250}$$

Simplify.

$$x-25=5\sqrt{10} x-25=-5\sqrt{10}$$

Add 25 to both sides of the equation.

$$x=5\sqrt{10}+25 x=25-5\sqrt{10}$$