Solve (2x)^2=(6/5x)^2+(7/20x+5/4x)^2

$$( 2 x ) ^ { 2 } = ( \frac { 6 } { 5 } x ) ^ { 2 } + ( \frac { 7 } { 20 } x + \frac { 5 } { 4 } x ) ^ { 2 }$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

Solution Steps

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

$$2^{2}x^{2}=\left(\frac{6}{5}x\right)^{2}+\left(\frac{7}{20}x+\frac{5}{4}x\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4x^{2}=\left(\frac{6}{5}x\right)^{2}+\left(\frac{7}{20}x+\frac{5}{4}x\right)^{2}$$

Expand \left(\frac{6}{5}x\right)^{2}.

$$4x^{2}=\left(\frac{6}{5}\right)^{2}x^{2}+\left(\frac{7}{20}x+\frac{5}{4}x\right)^{2}$$

Calculate \frac{6}{5} to the power of 2 and get \frac{36}{25}.

$$4x^{2}=\frac{36}{25}x^{2}+\left(\frac{7}{20}x+\frac{5}{4}x\right)^{2}$$

Combine \frac{7}{20}x and \frac{5}{4}x to get \frac{8}{5}x.

$$4x^{2}=\frac{36}{25}x^{2}+\left(\frac{8}{5}x\right)^{2}$$

Expand \left(\frac{8}{5}x\right)^{2}.

$$4x^{2}=\frac{36}{25}x^{2}+\left(\frac{8}{5}\right)^{2}x^{2}$$

Calculate \frac{8}{5} to the power of 2 and get \frac{64}{25}.

$$4x^{2}=\frac{36}{25}x^{2}+\frac{64}{25}x^{2}$$

Combine \frac{36}{25}x^{2} and \frac{64}{25}x^{2} to get 4x^{2}.

$$4x^{2}=4x^{2}$$

Subtract 4x^{2} from both sides.

$$4x^{2}-4x^{2}=0$$

Combine 4x^{2} and -4x^{2} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

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

$$2^{2}x^{2}=\left(\frac{6}{5}x\right)^{2}+\left(\frac{7}{20}x+\frac{5}{4}x\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4x^{2}=\left(\frac{6}{5}x\right)^{2}+\left(\frac{7}{20}x+\frac{5}{4}x\right)^{2}$$

Expand \left(\frac{6}{5}x\right)^{2}.

$$4x^{2}=\left(\frac{6}{5}\right)^{2}x^{2}+\left(\frac{7}{20}x+\frac{5}{4}x\right)^{2}$$

Calculate \frac{6}{5} to the power of 2 and get \frac{36}{25}.

$$4x^{2}=\frac{36}{25}x^{2}+\left(\frac{7}{20}x+\frac{5}{4}x\right)^{2}$$

Combine \frac{7}{20}x and \frac{5}{4}x to get \frac{8}{5}x.

$$4x^{2}=\frac{36}{25}x^{2}+\left(\frac{8}{5}x\right)^{2}$$

Expand \left(\frac{8}{5}x\right)^{2}.

$$4x^{2}=\frac{36}{25}x^{2}+\left(\frac{8}{5}\right)^{2}x^{2}$$

Calculate \frac{8}{5} to the power of 2 and get \frac{64}{25}.

$$4x^{2}=\frac{36}{25}x^{2}+\frac{64}{25}x^{2}$$

Combine \frac{36}{25}x^{2} and \frac{64}{25}x^{2} to get 4x^{2}.

$$4x^{2}=4x^{2}$$

Subtract 4x^{2} from both sides.

$$4x^{2}-4x^{2}=0$$

Combine 4x^{2} and -4x^{2} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$