Solve x^2^+36/x^2-12=0

$${ x }^{ { 2 }^{ } } + \frac{ 36 }{ { x }^{ 2 } } -12=0$$

Solve for x

$$x=\sqrt{6}\approx 2.449489743$$

$$x=-\sqrt{6}\approx -2.449489743$$

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 x^{2}.

$$x^{2}x^{2^{1}}+36+x^{2}\left(-12\right)=0$$

Calculate 2 to the power of 1 and get 2.

$$x^{2}x^{2}+36+x^{2}\left(-12\right)=0$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$x^{4}+36+x^{2}\left(-12\right)=0$$

Substitute t for x^{2}.

$$t^{2}-12t+36=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 1 for a, -12 for b, and 36 for c in the quadratic formula.

$$t=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 1\times 36}}{2}$$

Do the calculations.

$$t=\frac{12±0}{2}$$

Solutions are the same.

$$t=6$$

Since x=t^{2}, the solutions are obtained by evaluating x=±\sqrt{t} for positive t.

$$x=-\sqrt{6} x=\sqrt{6}$$