Solve x^2=8*10^-8/x^2+12+36

$${ x }^{ 2 } = \frac{ 8 \times { 10 }^{ -8 } }{ { x }^{ 2 } +12+36 }$$

Solve for x

$$x=-\frac{\sqrt{2\left(\sqrt{14400000002}-120000\right)}}{100}\approx -0.000040825$$

$$x=\frac{\sqrt{2\left(\sqrt{14400000002}-120000\right)}}{100}\approx 0.000040825$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by x^{2}+48.

$$\left(x^{2}+48\right)x^{2}=8\times 10^{-8}$$

Use the distributive property to multiply x^{2}+48 by x^{2}.

$$x^{4}+48x^{2}=8\times 10^{-8}$$

Calculate 10 to the power of -8 and get \frac{1}{100000000}.

$$x^{4}+48x^{2}=8\times \frac{1}{100000000}$$

Multiply 8 and \frac{1}{100000000} to get \frac{1}{12500000}.

$$x^{4}+48x^{2}=\frac{1}{12500000}$$

Subtract \frac{1}{12500000} from both sides.

$$x^{4}+48x^{2}-\frac{1}{12500000}=0$$

Substitute t for x^{2}.

$$t^{2}+48t-\frac{1}{12500000}=0$$

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, 48 for b, and -\frac{1}{12500000} for c in the quadratic formula.

$$t=\frac{-48±\sqrt{48^{2}-4\times 1\left(-\frac{1}{12500000}\right)}}{2}$$

Do the calculations.

$$t=\frac{-48±\frac{1}{2500}\sqrt{14400000002}}{2}$$

Solve the equation t=\frac{-48±\frac{1}{2500}\sqrt{14400000002}}{2} when ± is plus and when ± is minus.

$$t=\frac{\sqrt{14400000002}}{5000}-24 t=-\frac{\sqrt{14400000002}}{5000}-24$$

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

$$x=\frac{\sqrt{\frac{\sqrt{14400000002}}{2}-60000}}{50} x=-\frac{\sqrt{\frac{\sqrt{14400000002}}{2}-60000}}{50}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{2\left(\sqrt{14400000002}-120000\right)}}{100}\approx 0.000040825$$

$$x=-\frac{\sqrt{2\left(\sqrt{14400000002}-120000\right)}}{100}\approx -0.000040825$$

$$x=-\frac{i\sqrt{2\left(\sqrt{14400000002}+120000\right)}}{100}\approx -0-6.92820323i$$

$$x=\frac{i\sqrt{2\left(\sqrt{14400000002}+120000\right)}}{100}\approx 6.92820323i$$