Solve x^2+4/800=201

$$\frac { x ^ { 2 } + 4 } { 800 } = 201$$

Solve for x

$$x=2\sqrt{40199}\approx 400.993765538$$

$$x=-2\sqrt{40199}\approx -400.993765538$$

Steps by Finding Square Root

Multiply both sides by 800.

$$x^{2}+4=201\times 800$$

Multiply 201 and 800 to get 160800.

$$x^{2}+4=160800$$

Subtract 4 from both sides.

$$x^{2}=160800-4$$

Subtract 4 from 160800 to get 160796.

$$x^{2}=160796$$

Take the square root of both sides of the equation.

$$x=2\sqrt{40199} x=-2\sqrt{40199}$$

Steps Using the Quadratic Formula

Multiply both sides by 800.

$$x^{2}+4=201\times 800$$

Multiply 201 and 800 to get 160800.

$$x^{2}+4=160800$$

Subtract 160800 from both sides.

$$x^{2}+4-160800=0$$

Subtract 160800 from 4 to get -160796.

$$x^{2}-160796=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -160796 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-160796\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-160796\right)}}{2}$$

Multiply -4 times -160796.

$$x=\frac{0±\sqrt{643184}}{2}$$

Take the square root of 643184.

$$x=\frac{0±4\sqrt{40199}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{40199}}{2} when ± is plus.

$$x=2\sqrt{40199}$$

Now solve the equation x=\frac{0±4\sqrt{40199}}{2} when ± is minus.

$$x=-2\sqrt{40199}$$

The equation is now solved.

$$x=2\sqrt{40199} x=-2\sqrt{40199}$$