Solve 6/x^2-16/4x^2=1

$$\frac { 6 } { x ^ { 2 } } - \frac { 16 } { 4 x ^ { 2 } } = 1$$

Solve for x

$$x=\sqrt{2}\approx 1.414213562$$

$$x=-\sqrt{2}\approx -1.414213562$$

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 4x^{2}, the least common multiple of x^{2},4x^{2}.

$$4\times 6-16=4x^{2}$$

Multiply 4 and 6 to get 24.

$$24-16=4x^{2}$$

Subtract 16 from 24 to get 8.

$$8=4x^{2}$$

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

$$4x^{2}=8$$

Divide both sides by 4.

$$x^{2}=\frac{8}{4}$$

Divide 8 by 4 to get 2.

$$x^{2}=2$$

Take the square root of both sides of the equation.

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

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 4x^{2}, the least common multiple of x^{2},4x^{2}.

$$4\times 6-16=4x^{2}$$

Multiply 4 and 6 to get 24.

$$24-16=4x^{2}$$

Subtract 16 from 24 to get 8.

$$8=4x^{2}$$

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

$$4x^{2}=8$$

Subtract 8 from both sides.

$$4x^{2}-8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-8\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-8\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-8\right)}}{2\times 4}$$

Multiply -16 times -8.

$$x=\frac{0±\sqrt{128}}{2\times 4}$$

Take the square root of 128.

$$x=\frac{0±8\sqrt{2}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±8\sqrt{2}}{8}$$

Now solve the equation x=\frac{0±8\sqrt{2}}{8} when ± is plus.

$$x=\sqrt{2}$$

Now solve the equation x=\frac{0±8\sqrt{2}}{8} when ± is minus.

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

The equation is now solved.

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