Solve 0.377=-1/x^2*13.6

$$0.377=- \frac{ 1 }{ { x }^{ 2 } } \times 13.6$$

Solve for x (complex solution)

$$x=-\frac{i\times 20\sqrt{12818}}{377}\approx -0-6.006186024i$$

$$x=\frac{i\times 20\sqrt{12818}}{377}\approx 6.006186024i$$

Steps by Finding Square Root

Divide both sides by 13.6.

$$\frac{0.377}{13.6}=-\frac{1}{x^{2}}$$

Expand \frac{0.377}{13.6} by multiplying both numerator and the denominator by 1000.

$$\frac{377}{13600}=-\frac{1}{x^{2}}$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 13600x^{2}, the least common multiple of 13600,x^{2}.

$$377x^{2}=-13600$$

Divide both sides by 377.

$$x^{2}=-\frac{13600}{377}$$

The equation is now solved.

$$x=\frac{20\sqrt{12818}i}{377} x=-\frac{20\sqrt{12818}i}{377}$$

Steps Using the Quadratic Formula

Divide both sides by 13.6.

$$\frac{0.377}{13.6}=-\frac{1}{x^{2}}$$

Expand \frac{0.377}{13.6} by multiplying both numerator and the denominator by 1000.

$$\frac{377}{13600}=-\frac{1}{x^{2}}$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 13600x^{2}, the least common multiple of 13600,x^{2}.

$$377x^{2}=-13600$$

Add 13600 to both sides.

$$377x^{2}+13600=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 377 for a, 0 for b, and 13600 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 377\times 13600}}{2\times 377}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 377\times 13600}}{2\times 377}$$

Multiply -4 times 377.

$$x=\frac{0±\sqrt{-1508\times 13600}}{2\times 377}$$

Multiply -1508 times 13600.

$$x=\frac{0±\sqrt{-20508800}}{2\times 377}$$

Take the square root of -20508800.

$$x=\frac{0±40\sqrt{12818}i}{2\times 377}$$

Multiply 2 times 377.

$$x=\frac{0±40\sqrt{12818}i}{754}$$

Now solve the equation x=\frac{0±40\sqrt{12818}i}{754} when ± is plus.

$$x=\frac{20\sqrt{12818}i}{377}$$

Now solve the equation x=\frac{0±40\sqrt{12818}i}{754} when ± is minus.

$$x=-\frac{20\sqrt{12818}i}{377}$$

The equation is now solved.

$$x=\frac{20\sqrt{12818}i}{377} x=-\frac{20\sqrt{12818}i}{377}$$