Solve 2x/400=703/x+x/400

$$\frac{ 2x }{ 400 } = \frac{ 703 }{ x } + \frac{ x }{ 400 }$$

Solve for x

$$x=20\sqrt{703}\approx 530.282943343$$

$$x=-20\sqrt{703}\approx -530.282943343$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 400x, the least common multiple of 400,x.

$$x\times 2x=400\times 703+xx$$

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

$$x\times 2x=400\times 703+x^{2}$$

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

$$x^{2}\times 2=400\times 703+x^{2}$$

Multiply 400 and 703 to get 281200.

$$x^{2}\times 2=281200+x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}\times 2-x^{2}=281200$$

Combine x^{2}\times 2 and -x^{2} to get x^{2}.

$$x^{2}=281200$$

Take the square root of both sides of the equation.

$$x=20\sqrt{703} x=-20\sqrt{703}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 400x, the least common multiple of 400,x.

$$x\times 2x=400\times 703+xx$$

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

$$x\times 2x=400\times 703+x^{2}$$

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

$$x^{2}\times 2=400\times 703+x^{2}$$

Multiply 400 and 703 to get 281200.

$$x^{2}\times 2=281200+x^{2}$$

Subtract 281200 from both sides.

$$x^{2}\times 2-281200=x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}\times 2-281200-x^{2}=0$$

Combine x^{2}\times 2 and -x^{2} to get x^{2}.

$$x^{2}-281200=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -281200 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-281200\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-281200\right)}}{2}$$

Multiply -4 times -281200.

$$x=\frac{0±\sqrt{1124800}}{2}$$

Take the square root of 1124800.

$$x=\frac{0±40\sqrt{703}}{2}$$

Now solve the equation x=\frac{0±40\sqrt{703}}{2} when ± is plus.

$$x=20\sqrt{703}$$

Now solve the equation x=\frac{0±40\sqrt{703}}{2} when ± is minus.

$$x=-20\sqrt{703}$$

The equation is now solved.

$$x=20\sqrt{703} x=-20\sqrt{703}$$