Solve (5x)^2+(7x)^2-2(5x)*(7x)*3/5=(4x)^2

$$( 5 x ) ^ { 2 } + ( 7 x ) ^ { 2 } - 2 ( 5 x ) \cdot ( 7 x ) \cdot \frac { 3 } { 5 } = ( 4 x ) ^ { 2 }$$

Solve for x

$$x=0$$

Steps by Finding Square Root

Multiply x and x to get x^{2}.

$$\left(5x\right)^{2}+\left(7x\right)^{2}-2\times 5x^{2}\times 7\times \frac{3}{5}=\left(4x\right)^{2}$$

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

$$5^{2}x^{2}+\left(7x\right)^{2}-2\times 5x^{2}\times 7\times \frac{3}{5}=\left(4x\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25x^{2}+\left(7x\right)^{2}-2\times 5x^{2}\times 7\times \frac{3}{5}=\left(4x\right)^{2}$$

Expand \left(7x\right)^{2}.

$$25x^{2}+7^{2}x^{2}-2\times 5x^{2}\times 7\times \frac{3}{5}=\left(4x\right)^{2}$$

Calculate 7 to the power of 2 and get 49.

$$25x^{2}+49x^{2}-2\times 5x^{2}\times 7\times \frac{3}{5}=\left(4x\right)^{2}$$

Combine 25x^{2} and 49x^{2} to get 74x^{2}.

$$74x^{2}-2\times 5x^{2}\times 7\times \frac{3}{5}=\left(4x\right)^{2}$$

Multiply 2 and 5 to get 10.

$$74x^{2}-10x^{2}\times 7\times \frac{3}{5}=\left(4x\right)^{2}$$

Multiply 10 and 7 to get 70.

$$74x^{2}-70x^{2}\times \frac{3}{5}=\left(4x\right)^{2}$$

Multiply 70 and \frac{3}{5} to get 42.

$$74x^{2}-42x^{2}=\left(4x\right)^{2}$$

Combine 74x^{2} and -42x^{2} to get 32x^{2}.

$$32x^{2}=\left(4x\right)^{2}$$

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

$$32x^{2}=4^{2}x^{2}$$

Calculate 4 to the power of 2 and get 16.

$$32x^{2}=16x^{2}$$

Subtract 16x^{2} from both sides.

$$32x^{2}-16x^{2}=0$$

Combine 32x^{2} and -16x^{2} to get 16x^{2}.

$$16x^{2}=0$$

Divide both sides by 16. Zero divided by any non-zero number gives zero.

$$x^{2}=0$$

Take the square root of both sides of the equation.

$$x=0 x=0$$

The equation is now solved. Solutions are the same.

$$x=0$$

Steps Using the Quadratic Formula

Multiply x and x to get x^{2}.

$$\left(5x\right)^{2}+\left(7x\right)^{2}-2\times 5x^{2}\times 7\times \frac{3}{5}=\left(4x\right)^{2}$$

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

$$5^{2}x^{2}+\left(7x\right)^{2}-2\times 5x^{2}\times 7\times \frac{3}{5}=\left(4x\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25x^{2}+\left(7x\right)^{2}-2\times 5x^{2}\times 7\times \frac{3}{5}=\left(4x\right)^{2}$$

Expand \left(7x\right)^{2}.

$$25x^{2}+7^{2}x^{2}-2\times 5x^{2}\times 7\times \frac{3}{5}=\left(4x\right)^{2}$$

Calculate 7 to the power of 2 and get 49.

$$25x^{2}+49x^{2}-2\times 5x^{2}\times 7\times \frac{3}{5}=\left(4x\right)^{2}$$

Combine 25x^{2} and 49x^{2} to get 74x^{2}.

$$74x^{2}-2\times 5x^{2}\times 7\times \frac{3}{5}=\left(4x\right)^{2}$$

Multiply 2 and 5 to get 10.

$$74x^{2}-10x^{2}\times 7\times \frac{3}{5}=\left(4x\right)^{2}$$

Multiply 10 and 7 to get 70.

$$74x^{2}-70x^{2}\times \frac{3}{5}=\left(4x\right)^{2}$$

Multiply 70 and \frac{3}{5} to get 42.

$$74x^{2}-42x^{2}=\left(4x\right)^{2}$$

Combine 74x^{2} and -42x^{2} to get 32x^{2}.

$$32x^{2}=\left(4x\right)^{2}$$

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

$$32x^{2}=4^{2}x^{2}$$

Calculate 4 to the power of 2 and get 16.

$$32x^{2}=16x^{2}$$

Subtract 16x^{2} from both sides.

$$32x^{2}-16x^{2}=0$$

Combine 32x^{2} and -16x^{2} to get 16x^{2}.

$$16x^{2}=0$$

Divide both sides by 16. Zero divided by any non-zero number gives zero.

$$x^{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}}}{2}$$

Take the square root of 0^{2}.

$$x=\frac{0±0}{2}$$

Divide 0 by 2.

$$x=0$$