Solve left(28-2xright)left(20-2xright)=300

$$\left( 28-2x \right) \left( 20-2x \right) =300$$

Solve for x

$$x=12-\sqrt{79}\approx 3.111805583$$

$$x=\sqrt{79}+12\approx 20.888194417$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 28-2x by 20-2x and combine like terms.

$$560-96x+4x^{2}=300$$

Subtract 300 from both sides.

$$560-96x+4x^{2}-300=0$$

Subtract 300 from 560 to get 260.

$$260-96x+4x^{2}=0$$

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.

$$4x^{2}-96x+260=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, -96 for b, and 260 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-96\right)±\sqrt{\left(-96\right)^{2}-4\times 4\times 260}}{2\times 4}$$

Square -96.

$$x=\frac{-\left(-96\right)±\sqrt{9216-4\times 4\times 260}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{-\left(-96\right)±\sqrt{9216-16\times 260}}{2\times 4}$$

Multiply -16 times 260.

$$x=\frac{-\left(-96\right)±\sqrt{9216-4160}}{2\times 4}$$

Add 9216 to -4160.

$$x=\frac{-\left(-96\right)±\sqrt{5056}}{2\times 4}$$

Take the square root of 5056.

$$x=\frac{-\left(-96\right)±8\sqrt{79}}{2\times 4}$$

The opposite of -96 is 96.

$$x=\frac{96±8\sqrt{79}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{96±8\sqrt{79}}{8}$$

Now solve the equation x=\frac{96±8\sqrt{79}}{8} when ± is plus. Add 96 to 8\sqrt{79}.

$$x=\frac{8\sqrt{79}+96}{8}$$

Divide 96+8\sqrt{79} by 8.

$$x=\sqrt{79}+12$$

Now solve the equation x=\frac{96±8\sqrt{79}}{8} when ± is minus. Subtract 8\sqrt{79} from 96.

$$x=\frac{96-8\sqrt{79}}{8}$$

Divide 96-8\sqrt{79} by 8.

$$x=12-\sqrt{79}$$

The equation is now solved.

$$x=\sqrt{79}+12 x=12-\sqrt{79}$$

Steps for Completing the Square

Use the distributive property to multiply 28-2x by 20-2x and combine like terms.

$$560-96x+4x^{2}=300$$

Subtract 560 from both sides.

$$-96x+4x^{2}=300-560$$

Subtract 560 from 300 to get -260.

$$-96x+4x^{2}=-260$$

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.

$$4x^{2}-96x=-260$$

Divide both sides by 4.

$$\frac{4x^{2}-96x}{4}=-\frac{260}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x^{2}+\left(-\frac{96}{4}\right)x=-\frac{260}{4}$$

Divide -96 by 4.

$$x^{2}-24x=-\frac{260}{4}$$

Divide -260 by 4.

$$x^{2}-24x=-65$$

Divide -24, the coefficient of the x term, by 2 to get -12. Then add the square of -12 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-24x+\left(-12\right)^{2}=-65+\left(-12\right)^{2}$$

Square -12.

$$x^{2}-24x+144=-65+144$$

Add -65 to 144.

$$x^{2}-24x+144=79$$

Factor x^{2}-24x+144. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-12\right)^{2}=79$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-12\right)^{2}}=\sqrt{79}$$

Simplify.

$$x-12=\sqrt{79} x-12=-\sqrt{79}$$

Add 12 to both sides of the equation.

$$x=\sqrt{79}+12 x=12-\sqrt{79}$$