Solve x^2/4=x^2/9+4

$$\frac { x ^ { 2 } } { 4 } = \frac { x ^ { 2 } } { 9 } + 4$$

Solve for x

$$x = \frac{12 \sqrt{5}}{5} \approx 5.366563146$$

$$x = -\frac{12 \sqrt{5}}{5} \approx -5.366563146$$

Steps by Finding Square Root

Multiply both sides of the equation by 36, the least common multiple of 4,9.

$$9x^{2}=4x^{2}+144$$

Subtract 4x^{2} from both sides.

$$9x^{2}-4x^{2}=144$$

Combine 9x^{2} and -4x^{2} to get 5x^{2}.

$$5x^{2}=144$$

Divide both sides by 5.

$$x^{2}=\frac{144}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{12\sqrt{5}}{5} x=-\frac{12\sqrt{5}}{5}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 36, the least common multiple of 4,9.

$$9x^{2}=4x^{2}+144$$

Subtract 4x^{2} from both sides.

$$9x^{2}-4x^{2}=144$$

Combine 9x^{2} and -4x^{2} to get 5x^{2}.

$$5x^{2}=144$$

Subtract 144 from both sides.

$$5x^{2}-144=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -144 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-144\right)}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-144\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\left(-144\right)}}{2\times 5}$$

Multiply -20 times -144.

$$x=\frac{0±\sqrt{2880}}{2\times 5}$$

Take the square root of 2880.

$$x=\frac{0±24\sqrt{5}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±24\sqrt{5}}{10}$$

Now solve the equation x=\frac{0±24\sqrt{5}}{10} when ± is plus.

$$x=\frac{12\sqrt{5}}{5}$$

Now solve the equation x=\frac{0±24\sqrt{5}}{10} when ± is minus.

$$x=-\frac{12\sqrt{5}}{5}$$

The equation is now solved.

$$x=\frac{12\sqrt{5}}{5} x=-\frac{12\sqrt{5}}{5}$$