Solve x^2/81-1^2/9=1

$$\frac { x ^ { 2 } } { 81 } - \frac { 1 ^ { 2 } } { 9 } = 1$$

Solve for x

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

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

Steps by Finding Square Root

Multiply both sides of the equation by 81, the least common multiple of 81,9.

$$x^{2}-9\times 1^{2}=81$$

Calculate 1 to the power of 2 and get 1.

$$x^{2}-9=81$$

Add 9 to both sides.

$$x^{2}=81+9$$

Add 81 and 9 to get 90.

$$x^{2}=90$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Multiply both sides of the equation by 81, the least common multiple of 81,9.

$$x^{2}-9\times 1^{2}=81$$

Calculate 1 to the power of 2 and get 1.

$$x^{2}-9=81$$

Subtract 81 from both sides.

$$x^{2}-9-81=0$$

Subtract 81 from -9 to get -90.

$$x^{2}-90=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -90 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-90\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-90\right)}}{2}$$

Multiply -4 times -90.

$$x=\frac{0±\sqrt{360}}{2}$$

Take the square root of 360.

$$x=\frac{0±6\sqrt{10}}{2}$$

Now solve the equation x=\frac{0±6\sqrt{10}}{2} when ± is plus.

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

Now solve the equation x=\frac{0±6\sqrt{10}}{2} when ± is minus.

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

The equation is now solved.

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