Solve 18div(18+x)*18+x=18

$$18 \div (18+x) \times 18+x=18$$

Solve for x

$$x=0$$

Steps by Finding Square Root

Variable x cannot be equal to -18 since division by zero is not defined. Multiply both sides of the equation by x+18.

$$18\times 18+\left(x+18\right)x=18\left(x+18\right)$$

Multiply 18 and 18 to get 324.

$$324+\left(x+18\right)x=18\left(x+18\right)$$

Use the distributive property to multiply x+18 by x.

$$324+x^{2}+18x=18\left(x+18\right)$$

Use the distributive property to multiply 18 by x+18.

$$324+x^{2}+18x=18x+324$$

Subtract 18x from both sides.

$$324+x^{2}+18x-18x=324$$

Combine 18x and -18x to get 0.

$$324+x^{2}=324$$

Subtract 324 from both sides.

$$x^{2}=324-324$$

Subtract 324 from 324 to get 0.

$$x^{2}=0$$

Take the square root of both sides of the equation.

$$x=0 x=0$$

The equation is now solved. Solutions are the same.

$$x=0$$

Steps Using the Quadratic Formula

Variable x cannot be equal to -18 since division by zero is not defined. Multiply both sides of the equation by x+18.

$$18\times 18+\left(x+18\right)x=18\left(x+18\right)$$

Multiply 18 and 18 to get 324.

$$324+\left(x+18\right)x=18\left(x+18\right)$$

Use the distributive property to multiply x+18 by x.

$$324+x^{2}+18x=18\left(x+18\right)$$

Use the distributive property to multiply 18 by x+18.

$$324+x^{2}+18x=18x+324$$

Subtract 18x from both sides.

$$324+x^{2}+18x-18x=324$$

Combine 18x and -18x to get 0.

$$324+x^{2}=324$$

Subtract 324 from both sides.

$$324+x^{2}-324=0$$

Subtract 324 from 324 to get 0.

$$x^{2}=0$$

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

$$x=\frac{0±\sqrt{0^{2}}}{2}$$

Take the square root of 0^{2}.

$$x=\frac{0±0}{2}$$

Divide 0 by 2.

$$x=0$$