Solve 800=(40+x)(20+x)

$$800 = ( 40 + x ) ( 20 + x )$$

Solve for x

$$x=-60$$

$$x=0$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 40+x by 20+x and combine like terms.

$$800=800+60x+x^{2}$$

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

$$800+60x+x^{2}=800$$

Subtract 800 from both sides.

$$800+60x+x^{2}-800=0$$

Subtract 800 from 800 to get 0.

$$60x+x^{2}=0$$

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.

$$x^{2}+60x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 60 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-60±\sqrt{60^{2}}}{2}$$

Take the square root of 60^{2}.

$$x=\frac{-60±60}{2}$$

Now solve the equation x=\frac{-60±60}{2} when ± is plus. Add -60 to 60.

$$x=\frac{0}{2}$$

Divide 0 by 2.

$$x=0$$

Now solve the equation x=\frac{-60±60}{2} when ± is minus. Subtract 60 from -60.

$$x=-\frac{120}{2}$$

Divide -120 by 2.

$$x=-60$$

The equation is now solved.

$$x=0 x=-60$$

Steps for Completing the Square

Use the distributive property to multiply 40+x by 20+x and combine like terms.

$$800=800+60x+x^{2}$$

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

$$800+60x+x^{2}=800$$

Subtract 800 from both sides.

$$60x+x^{2}=800-800$$

Subtract 800 from 800 to get 0.

$$60x+x^{2}=0$$

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.

$$x^{2}+60x=0$$

Divide 60, the coefficient of the x term, by 2 to get 30. Then add the square of 30 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+60x+30^{2}=30^{2}$$

Square 30.

$$x^{2}+60x+900=900$$

Factor x^{2}+60x+900. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+30\right)^{2}=900$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+30\right)^{2}}=\sqrt{900}$$

Simplify.

$$x+30=30 x+30=-30$$

Subtract 30 from both sides of the equation.

$$x=0 x=-60$$