Solve 10^4(4x+0,2)=10*(10sqrt{2})^2+400

$$10 ^ { 4 } ( 4 x + 0,2 ) = 10 \cdot ( 10 \sqrt { 2 } ) ^ { 2 } + 400$$

Solve for x

$$x=0,01$$

Steps for Solving Linear Equation

Calculate 10 to the power of 4 and get 10000.

$$10000\left(4x+0,2\right)=10\times \left(10\sqrt{2}\right)^{2}+400$$

Use the distributive property to multiply 10000 by 4x+0,2.

$$40000x+2000=10\times \left(10\sqrt{2}\right)^{2}+400$$

Expand \left(10\sqrt{2}\right)^{2}.

$$40000x+2000=10\times 10^{2}\left(\sqrt{2}\right)^{2}+400$$

Calculate 10 to the power of 2 and get 100.

$$40000x+2000=10\times 100\left(\sqrt{2}\right)^{2}+400$$

The square of \sqrt{2} is 2.

$$40000x+2000=10\times 100\times 2+400$$

Multiply 100 and 2 to get 200.

$$40000x+2000=10\times 200+400$$

Multiply 10 and 200 to get 2000.

$$40000x+2000=2000+400$$

Add 2000 and 400 to get 2400.

$$40000x+2000=2400$$

Subtract 2000 from both sides.

$$40000x=2400-2000$$

Subtract 2000 from 2400 to get 400.

$$40000x=400$$

Divide both sides by 40000.

$$x=\frac{400}{40000}$$

Reduce the fraction \frac{400}{40000} to lowest terms by extracting and canceling out 400.

$$x=\frac{1}{100}$$