Solve 1=1/160x^2+4

$$1 = \frac { 1 } { 160 } x ^ { 2 } + 4$$

Solve for x (complex solution)

$$x=-4\sqrt{30}i\approx -0-21.9089023i$$

$$x=4\sqrt{30}i\approx 21.9089023i$$

Steps by Finding Square Root

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

$$\frac{1}{160}x^{2}+4=1$$

Subtract 4 from both sides.

$$\frac{1}{160}x^{2}=1-4$$

Subtract 4 from 1 to get -3.

$$\frac{1}{160}x^{2}=-3$$

Multiply both sides by 160, the reciprocal of \frac{1}{160}.

$$x^{2}=-3\times 160$$

Multiply -3 and 160 to get -480.

$$x^{2}=-480$$

The equation is now solved.

$$x=4\sqrt{30}i x=-4\sqrt{30}i$$

Steps Using the Quadratic Formula

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

$$\frac{1}{160}x^{2}+4=1$$

Subtract 1 from both sides.

$$\frac{1}{160}x^{2}+4-1=0$$

Subtract 1 from 4 to get 3.

$$\frac{1}{160}x^{2}+3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1}{160} for a, 0 for b, and 3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{160}\times 3}}{2\times \frac{1}{160}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{1}{160}\times 3}}{2\times \frac{1}{160}}$$

Multiply -4 times \frac{1}{160}.

$$x=\frac{0±\sqrt{-\frac{1}{40}\times 3}}{2\times \frac{1}{160}}$$

Multiply -\frac{1}{40} times 3.

$$x=\frac{0±\sqrt{-\frac{3}{40}}}{2\times \frac{1}{160}}$$

Take the square root of -\frac{3}{40}.

$$x=\frac{0±\frac{\sqrt{30}i}{20}}{2\times \frac{1}{160}}$$

Multiply 2 times \frac{1}{160}.

$$x=\frac{0±\frac{\sqrt{30}i}{20}}{\frac{1}{80}}$$

Now solve the equation x=\frac{0±\frac{\sqrt{30}i}{20}}{\frac{1}{80}} when ± is plus.

$$x=4\sqrt{30}i$$

Now solve the equation x=\frac{0±\frac{\sqrt{30}i}{20}}{\frac{1}{80}} when ± is minus.

$$x=-4\sqrt{30}i$$

The equation is now solved.

$$x=4\sqrt{30}i x=-4\sqrt{30}i$$