Solve sqrt{02}(5-04)^2=M*(sqrt{02}*5-04)^2

$$\sqrt { 02 } ( 5 - 04 ) ^ { 2 } = M \cdot ( \sqrt { 02 } \times 5 - 04 ) ^ { 2 }$$

Solve for M (complex solution)

$$M\in \mathrm{C}$$

Solution Steps

Multiply 0 and 2 to get 0.

$$\sqrt{0}\left(5-0\times 4\right)^{2}=M\left(5\sqrt{0\times 2}-0\times 4\right)^{2}$$

Calculate the square root of 0 and get 0.

$$0\left(5-0\times 4\right)^{2}=M\left(5\sqrt{0\times 2}-0\times 4\right)^{2}$$

Multiply 0 and 4 to get 0.

$$0\left(5-0\right)^{2}=M\left(5\sqrt{0\times 2}-0\times 4\right)^{2}$$

Subtract 0 from 5 to get 5.

$$0\times 5^{2}=M\left(5\sqrt{0\times 2}-0\times 4\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$0\times 25=M\left(5\sqrt{0\times 2}-0\times 4\right)^{2}$$

Multiply 0 and 25 to get 0.

$$0=M\left(5\sqrt{0\times 2}-0\times 4\right)^{2}$$

Multiply 0 and 2 to get 0.

$$0=M\left(5\sqrt{0}-0\times 4\right)^{2}$$

Calculate the square root of 0 and get 0.

$$0=M\left(5\times 0-0\times 4\right)^{2}$$

Multiply 5 and 0 to get 0.

$$0=M\left(0-0\times 4\right)^{2}$$

Multiply 0 and 4 to get 0.

$$0=M\left(0-0\right)^{2}$$

Subtracting 0 from itself leaves 0.

$$0=M\times 0^{2}$$

Calculate 0 to the power of 2 and get 0.

$$0=M\times 0$$

Anything times zero gives zero.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any M.

$$M\in \mathrm{C}$$

Solve for M

$$M\in \mathrm{R}$$

Solution Steps

Multiply 0 and 2 to get 0.

$$\sqrt{0}\left(5-0\times 4\right)^{2}=M\left(5\sqrt{0\times 2}-0\times 4\right)^{2}$$

Calculate the square root of 0 and get 0.

$$0\left(5-0\times 4\right)^{2}=M\left(5\sqrt{0\times 2}-0\times 4\right)^{2}$$

Multiply 0 and 4 to get 0.

$$0\left(5-0\right)^{2}=M\left(5\sqrt{0\times 2}-0\times 4\right)^{2}$$

Subtract 0 from 5 to get 5.

$$0\times 5^{2}=M\left(5\sqrt{0\times 2}-0\times 4\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$0\times 25=M\left(5\sqrt{0\times 2}-0\times 4\right)^{2}$$

Multiply 0 and 25 to get 0.

$$0=M\left(5\sqrt{0\times 2}-0\times 4\right)^{2}$$

Multiply 0 and 2 to get 0.

$$0=M\left(5\sqrt{0}-0\times 4\right)^{2}$$

Calculate the square root of 0 and get 0.

$$0=M\left(5\times 0-0\times 4\right)^{2}$$

Multiply 5 and 0 to get 0.

$$0=M\left(0-0\times 4\right)^{2}$$

Multiply 0 and 4 to get 0.

$$0=M\left(0-0\right)^{2}$$

Subtracting 0 from itself leaves 0.

$$0=M\times 0^{2}$$

Calculate 0 to the power of 2 and get 0.

$$0=M\times 0$$

Anything times zero gives zero.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any M.

$$M\in \mathrm{R}$$