Solve x^2+23040000/x^2=10000

$$x ^ { 2 } + \frac { 23040000 } { x ^ { 2 } } = 10000$$

Solve for x

$$x=-60$$

$$x=60$$

$$x=80$$

$$x=-80$$

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}.

$$x^{2}x^{2}[phone]=10000x^{2}$$

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

$$x^{4}[phone]=10000x^{2}$$

Subtract 10000x^{2} from both sides.

$$x^{4}[phone]x^{2}=0$$

Substitute t for x^{2}.

$$t^{2}-10000t+23040000=0$$

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, -10000 for b, and 23040000 for c in the quadratic formula.

$$t=\frac{-\left(-10000\right)±\sqrt{\left(-10000\right)^{2}-4\times 1\times 23040000}}{2}$$

Do the calculations.

$$t=\frac{10000±2800}{2}$$

Solve the equation t=\frac{10000±2800}{2} when ± is plus and when ± is minus.

$$t=6400 t=3600$$

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

$$x=80 x=-80 x=60 x=-60$$