Solve 4/x^2=1/9

$$\frac { 4 } { x ^ { 2 } } = \frac { 1 } { 9 }$$

Solve for x

$$x=6$$

$$x=-6$$

Steps Using Difference of Squares

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 9x^{2}, the least common multiple of x^{2},9.

$$9\times 4=x^{2}$$

Multiply 9 and 4 to get 36.

$$36=x^{2}$$

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

$$x^{2}=36$$

Subtract 36 from both sides.

$$x^{2}-36=0$$

Consider x^{2}-36. Rewrite x^{2}-36 as x^{2}-6^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-6\right)\left(x+6\right)=0$$

To find equation solutions, solve x-6=0 and x+6=0.

$$x=6 x=-6$$

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 9x^{2}, the least common multiple of x^{2},9.

$$9\times 4=x^{2}$$

Multiply 9 and 4 to get 36.

$$36=x^{2}$$

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

$$x^{2}=36$$

Take the square root of both sides of the equation.

$$x=6 x=-6$$

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 9x^{2}, the least common multiple of x^{2},9.

$$9\times 4=x^{2}$$

Multiply 9 and 4 to get 36.

$$36=x^{2}$$

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

$$x^{2}=36$$

Subtract 36 from both sides.

$$x^{2}-36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-36\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-36\right)}}{2}$$

Multiply -4 times -36.

$$x=\frac{0±\sqrt{144}}{2}$$

Take the square root of 144.

$$x=\frac{0±12}{2}$$

Now solve the equation x=\frac{0±12}{2} when ± is plus. Divide 12 by 2.

$$x=6$$

Now solve the equation x=\frac{0±12}{2} when ± is minus. Divide -12 by 2.

$$x=-6$$

The equation is now solved.

$$x=6 x=-6$$