Solve 3-6/x^2=11/2

$$3 - \frac { 6 } { x ^ { 2 } } = 1 \frac { 1 } { 2 }$$

Solve for x

$$x=2$$

$$x=-2$$

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

$$2x^{2}\times 3-2\times 6=x^{2}\left(1\times 2+1\right)$$

Multiply 2 and 3 to get 6.

$$6x^{2}-2\times 6=x^{2}\left(1\times 2+1\right)$$

Multiply -2 and 6 to get -12.

$$6x^{2}-12=x^{2}\left(1\times 2+1\right)$$

Multiply 1 and 2 to get 2.

$$6x^{2}-12=x^{2}\left(2+1\right)$$

Add 2 and 1 to get 3.

$$6x^{2}-12=x^{2}\times 3$$

Subtract x^{2}\times 3 from both sides.

$$6x^{2}-12-x^{2}\times 3=0$$

Combine 6x^{2} and -x^{2}\times 3 to get 3x^{2}.

$$3x^{2}-12=0$$

Divide both sides by 3.

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

Consider x^{2}-4. Rewrite x^{2}-4 as x^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-2\right)\left(x+2\right)=0$$

To find equation solutions, solve x-2=0 and x+2=0.

$$x=2 x=-2$$

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

$$2x^{2}\times 3-2\times 6=x^{2}\left(1\times 2+1\right)$$

Multiply 2 and 3 to get 6.

$$6x^{2}-2\times 6=x^{2}\left(1\times 2+1\right)$$

Multiply -2 and 6 to get -12.

$$6x^{2}-12=x^{2}\left(1\times 2+1\right)$$

Multiply 1 and 2 to get 2.

$$6x^{2}-12=x^{2}\left(2+1\right)$$

Add 2 and 1 to get 3.

$$6x^{2}-12=x^{2}\times 3$$

Subtract x^{2}\times 3 from both sides.

$$6x^{2}-12-x^{2}\times 3=0$$

Combine 6x^{2} and -x^{2}\times 3 to get 3x^{2}.

$$3x^{2}-12=0$$

Add 12 to both sides. Anything plus zero gives itself.

$$3x^{2}=12$$

Divide both sides by 3.

$$x^{2}=\frac{12}{3}$$

Divide 12 by 3 to get 4.

$$x^{2}=4$$

Take the square root of both sides of the equation.

$$x=2 x=-2$$

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

$$2x^{2}\times 3-2\times 6=x^{2}\left(1\times 2+1\right)$$

Multiply 2 and 3 to get 6.

$$6x^{2}-2\times 6=x^{2}\left(1\times 2+1\right)$$

Multiply -2 and 6 to get -12.

$$6x^{2}-12=x^{2}\left(1\times 2+1\right)$$

Multiply 1 and 2 to get 2.

$$6x^{2}-12=x^{2}\left(2+1\right)$$

Add 2 and 1 to get 3.

$$6x^{2}-12=x^{2}\times 3$$

Subtract x^{2}\times 3 from both sides.

$$6x^{2}-12-x^{2}\times 3=0$$

Combine 6x^{2} and -x^{2}\times 3 to get 3x^{2}.

$$3x^{2}-12=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-12\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-12\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-12\right)}}{2\times 3}$$

Multiply -12 times -12.

$$x=\frac{0±\sqrt{144}}{2\times 3}$$

Take the square root of 144.

$$x=\frac{0±12}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±12}{6}$$

Now solve the equation x=\frac{0±12}{6} when ± is plus. Divide 12 by 6.

$$x=2$$

Now solve the equation x=\frac{0±12}{6} when ± is minus. Divide -12 by 6.

$$x=-2$$

The equation is now solved.

$$x=2 x=-2$$