Solve (45+3)*9sqrt{459529x}=10000x

$$(45+3) \times 9 \sqrt{ 459529x } =10000x$$

Solve for x

$$x = \frac{334996641}{390625} = 857\frac{231016}{390625} = 857.59140096$$

$$x=0$$

Solution Steps

Square both sides of the equation.

$$\left(9\left(45+3\right)\sqrt{459529x}\right)^{2}=\left(10000x\right)^{2}$$

Add 45 and 3 to get 48.

$$\left(9\times 48\sqrt{459529x}\right)^{2}=\left(10000x\right)^{2}$$

Multiply 9 and 48 to get 432.

$$\left(432\sqrt{459529x}\right)^{2}=\left(10000x\right)^{2}$$

Expand \left(432\sqrt{459529x}\right)^{2}.

$$432^{2}\left(\sqrt{459529x}\right)^{2}=\left(10000x\right)^{2}$$

Calculate 432 to the power of 2 and get 186624.

$$186624\left(\sqrt{459529x}\right)^{2}=\left(10000x\right)^{2}$$

Calculate \sqrt{459529x} to the power of 2 and get 459529x.

$$186624\times 459529x=\left(10000x\right)^{2}$$

Multiply 186624 and 459529 to get 85759140096.

$$85759140096x=\left(10000x\right)^{2}$$

Expand \left(10000x\right)^{2}.

$$85759140096x=10000^{2}x^{2}$$

Calculate 10000 to the power of 2 and get 100000000.

$$85759140096x=100000000x^{2}$$

Subtract 100000000x^{2} from both sides.

$$85759140096x-100000000x^{2}=0$$

Factor out x.

$$x\left(85759140096-100000000x\right)=0$$

To find equation solutions, solve x=0 and 85759140096-100000000x=0.

$$x=0 x=\frac{334996641}{390625}$$

Substitute 0 for x in the equation 9\left(45+3\right)\sqrt{459529x}=10000x.

$$9\left(45+3\right)\sqrt{459529\times 0}=10000\times 0$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute \frac{334996641}{390625} for x in the equation 9\left(45+3\right)\sqrt{459529x}=10000x.

$$9\left(45+3\right)\sqrt{459529\times \frac{334996641}{390625}}=10000\times \frac{334996641}{390625}$$

Simplify. The value x=\frac{334996641}{390625} satisfies the equation.

$$\frac{5359946256}{625}=\frac{5359946256}{625}$$

List all solutions of 432\sqrt{459529x}=10000x.

$$x=0 x=\frac{334996641}{390625}$$