Solve 25=355*200x^2/4*1000^2

$$25=355 \times 200 \frac{ { x }^{ 2 } }{ 4 \times { 1000 }^{ 2 } }$$

Solve for x

$$x = \frac{100 \sqrt{710}}{71} \approx 37.529331252$$

$$x = -\frac{100 \sqrt{710}}{71} \approx -37.529331252$$

Steps by Finding Square Root

Multiply 355 and 200 to get 71000.

$$25=71000\times \frac{x^{2}}{4\times 1000^{2}}$$

Calculate 1000 to the power of 2 and get 1000000.

$$25=71000\times \frac{x^{2}}{4\times 1000000}$$

Multiply 4 and 1000000 to get 4000000.

$$25=71000\times \frac{x^{2}}{4000000}$$

Express 71000\times \frac{x^{2}}{4000000} as a single fraction.

$$25=\frac{71000x^{2}}{4000000}$$

Divide 71000x^{2} by 4000000 to get \frac{71}{4000}x^{2}.

$$25=\frac{71}{4000}x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{71}{4000}x^{2}=25$$

Multiply both sides by \frac{4000}{71}, the reciprocal of \frac{71}{4000}.

$$x^{2}=25\times \frac{4000}{71}$$

Multiply 25 and \frac{4000}{71} to get \frac{100000}{71}.

$$x^{2}=\frac{100000}{71}$$

Take the square root of both sides of the equation.

$$x=\frac{100\sqrt{710}}{71} x=-\frac{100\sqrt{710}}{71}$$

Steps Using the Quadratic Formula

Multiply 355 and 200 to get 71000.

$$25=71000\times \frac{x^{2}}{4\times 1000^{2}}$$

Calculate 1000 to the power of 2 and get 1000000.

$$25=71000\times \frac{x^{2}}{4\times 1000000}$$

Multiply 4 and 1000000 to get 4000000.

$$25=71000\times \frac{x^{2}}{4000000}$$

Express 71000\times \frac{x^{2}}{4000000} as a single fraction.

$$25=\frac{71000x^{2}}{4000000}$$

Divide 71000x^{2} by 4000000 to get \frac{71}{4000}x^{2}.

$$25=\frac{71}{4000}x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{71}{4000}x^{2}=25$$

Subtract 25 from both sides.

$$\frac{71}{4000}x^{2}-25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{71}{4000} for a, 0 for b, and -25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{71}{4000}\left(-25\right)}}{2\times \frac{71}{4000}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{71}{4000}\left(-25\right)}}{2\times \frac{71}{4000}}$$

Multiply -4 times \frac{71}{4000}.

$$x=\frac{0±\sqrt{-\frac{71}{1000}\left(-25\right)}}{2\times \frac{71}{4000}}$$

Multiply -\frac{71}{1000} times -25.

$$x=\frac{0±\sqrt{\frac{71}{40}}}{2\times \frac{71}{4000}}$$

Take the square root of \frac{71}{40}.

$$x=\frac{0±\frac{\sqrt{710}}{20}}{2\times \frac{71}{4000}}$$

Multiply 2 times \frac{71}{4000}.

$$x=\frac{0±\frac{\sqrt{710}}{20}}{\frac{71}{2000}}$$

Now solve the equation x=\frac{0±\frac{\sqrt{710}}{20}}{\frac{71}{2000}} when ± is plus.

$$x=\frac{100\sqrt{710}}{71}$$

Now solve the equation x=\frac{0±\frac{\sqrt{710}}{20}}{\frac{71}{2000}} when ± is minus.

$$x=-\frac{100\sqrt{710}}{71}$$

The equation is now solved.

$$x=\frac{100\sqrt{710}}{71} x=-\frac{100\sqrt{710}}{71}$$