Solve x^2/81+x^2/16=pm2

$$\frac { x ^ { 2 } } { 81 } + \frac { x ^ { 2 } } { 16 } = \pm 2$$

Solve for x (complex solution)

$$x=-\frac{36i\sqrt{-97\left(±2\right)}}{97}$$

$$x=\frac{36i\sqrt{-97\left(±2\right)}}{97}$$

Steps by Finding Square Root

Multiply both sides of the equation by 1296, the least common multiple of 81,16.

$$16x^{2}+81x^{2}=1296\left(±2\right)$$

Combine 16x^{2} and 81x^{2} to get 97x^{2}.

$$97x^{2}=1296\left(±2\right)$$

Dividing by 97 undoes the multiplication by 97.

$$x^{2}=\frac{1296\left(±2\right)}{97}$$

Take the square root of both sides of the equation.

$$x=\frac{36\sqrt{97\left(±2\right)}}{97} x=-\frac{36\sqrt{97\left(±2\right)}}{97}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 1296, the least common multiple of 81,16.

$$16x^{2}+81x^{2}=1296\left(±2\right)$$

Combine 16x^{2} and 81x^{2} to get 97x^{2}.

$$97x^{2}=1296\left(±2\right)$$

Subtract 1296\left(±2\right) from both sides.

$$97x^{2}-1296\left(±2\right)=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 97 for a, 0 for b, and -1296\left(±2\right) for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 97\left(-1296\left(±2\right)\right)}}{2\times 97}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 97\left(-1296\left(±2\right)\right)}}{2\times 97}$$

Multiply -4 times 97.

$$x=\frac{0±\sqrt{-388\left(-1296\left(±2\right)\right)}}{2\times 97}$$

Multiply -388 times -1296\left(±2\right).

$$x=\frac{0±\sqrt{502848\left(±2\right)}}{2\times 97}$$

Take the square root of 502848\left(±2\right).

$$x=\frac{0±72\sqrt{97\left(±2\right)}}{2\times 97}$$

Multiply 2 times 97.

$$x=\frac{0±72\sqrt{97\left(±2\right)}}{194}$$

Now solve the equation x=\frac{0±72\sqrt{97\left(±2\right)}}{194} when ± is plus.

$$x=\frac{36\sqrt{97\left(±2\right)}}{97}$$

Now solve the equation x=\frac{0±72\sqrt{97\left(±2\right)}}{194} when ± is minus.

$$x=-\frac{36\sqrt{97\left(±2\right)}}{97}$$

The equation is now solved.

$$x=\frac{36\sqrt{97\left(±2\right)}}{97} x=-\frac{36\sqrt{97\left(±2\right)}}{97}$$

Solve for x

$$x=\frac{36\sqrt{97\left(±2\right)}}{97}$$

$$x=-\frac{36\sqrt{97\left(±2\right)}}{97}\text{, }\frac{5184\left(±2\right)}{97}\geq 0$$