Solve 0.09(x+30)=[0.3(x+30)]^2/x+50

$$0.09 ( x + 30 ) = \frac { [ 0.3 ( x + 30 ) ] ^ { 2 } } { x + 50 }$$

Solve for x

$$x=-30$$

Steps for Solving Linear Equation

Variable x cannot be equal to -50 since division by zero is not defined. Multiply both sides of the equation by x+50.

$$0.09\left(x+30\right)\left(x+50\right)=\left(0.3\left(x+30\right)\right)^{2}$$

Use the distributive property to multiply 0.09 by x+30.

$$\left(0.09x+2.7\right)\left(x+50\right)=\left(0.3\left(x+30\right)\right)^{2}$$

Use the distributive property to multiply 0.09x+2.7 by x+50 and combine like terms.

$$0.09x^{2}+7.2x+135=\left(0.3\left(x+30\right)\right)^{2}$$

Use the distributive property to multiply 0.3 by x+30.

$$0.09x^{2}+7.2x+135=\left(0.3x+9\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(0.3x+9\right)^{2}.

$$0.09x^{2}+7.2x+135=0.09x^{2}+5.4x+81$$

Subtract 0.09x^{2} from both sides.

$$0.09x^{2}+7.2x+135-0.09x^{2}=5.4x+81$$

Combine 0.09x^{2} and -0.09x^{2} to get 0.

$$7.2x+135=5.4x+81$$

Subtract 5.4x from both sides.

$$7.2x+135-5.4x=81$$

Combine 7.2x and -5.4x to get 1.8x.

$$1.8x+135=81$$

Subtract 135 from both sides.

$$1.8x=81-135$$

Subtract 135 from 81 to get -54.

$$1.8x=-54$$

Divide both sides by 1.8.

$$x=\frac{-54}{1.8}$$

Expand \frac{-54}{1.8} by multiplying both numerator and the denominator by 10.

$$x=\frac{-540}{18}$$

Divide -540 by 18 to get -30.

$$x=-30$$