Solve 30^2/x^2+x^2=10^2

$$\frac { 30 ^ { 2 } } { x ^ { 2 } } + x ^ { 2 } = 10 ^ { 2 }$$

Solve for x

$$x=-\sqrt{10}\approx -3.16227766$$

$$x=\sqrt{10}\approx 3.16227766$$

$$x=3\sqrt{10}\approx 9.486832981$$

$$x=-3\sqrt{10}\approx -9.486832981$$

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}.

$$30^{2}+x^{2}x^{2}=x^{2}\times 10^{2}$$

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

$$30^{2}+x^{4}=x^{2}\times 10^{2}$$

Calculate 30 to the power of 2 and get 900.

$$900+x^{4}=x^{2}\times 10^{2}$$

Calculate 10 to the power of 2 and get 100.

$$900+x^{4}=x^{2}\times 100$$

Subtract x^{2}\times 100 from both sides.

$$900+x^{4}-x^{2}\times 100=0$$

Multiply -1 and 100 to get -100.

$$900+x^{4}-100x^{2}=0$$

Substitute t for x^{2}.

$$t^{2}-100t+900=0$$

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, -100 for b, and 900 for c in the quadratic formula.

$$t=\frac{-\left(-100\right)±\sqrt{\left(-100\right)^{2}-4\times 1\times 900}}{2}$$

Do the calculations.

$$t=\frac{100±80}{2}$$

Solve the equation t=\frac{100±80}{2} when ± is plus and when ± is minus.

$$t=90 t=10$$

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

$$x=3\sqrt{10} x=-3\sqrt{10} x=\sqrt{10} x=-\sqrt{10}$$