Solve (3x)^2+(4x)^2=(5x)^2

$$( 3 x ) ^ { 2 } + ( 4 x ) ^ { 2 } = ( 5 x ) ^ { 2 }$$

Solve for x (complex solution)

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

Solution Steps

Expand \left(3x\right)^{2}.

$$3^{2}x^{2}+\left(4x\right)^{2}=\left(5x\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9x^{2}+\left(4x\right)^{2}=\left(5x\right)^{2}$$

Expand \left(4x\right)^{2}.

$$9x^{2}+4^{2}x^{2}=\left(5x\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$9x^{2}+16x^{2}=\left(5x\right)^{2}$$

Combine 9x^{2} and 16x^{2} to get 25x^{2}.

$$25x^{2}=\left(5x\right)^{2}$$

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

$$25x^{2}=5^{2}x^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25x^{2}=25x^{2}$$

Subtract 25x^{2} from both sides.

$$25x^{2}-25x^{2}=0$$

Combine 25x^{2} and -25x^{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(3x\right)^{2}.

$$3^{2}x^{2}+\left(4x\right)^{2}=\left(5x\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9x^{2}+\left(4x\right)^{2}=\left(5x\right)^{2}$$

Expand \left(4x\right)^{2}.

$$9x^{2}+4^{2}x^{2}=\left(5x\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$9x^{2}+16x^{2}=\left(5x\right)^{2}$$

Combine 9x^{2} and 16x^{2} to get 25x^{2}.

$$25x^{2}=\left(5x\right)^{2}$$

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

$$25x^{2}=5^{2}x^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25x^{2}=25x^{2}$$

Subtract 25x^{2} from both sides.

$$25x^{2}-25x^{2}=0$$

Combine 25x^{2} and -25x^{2} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

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