Solve x^2/16+x^2/12=1

$$\frac{ { x }^{ 2 } }{ 16 } + \frac{ { x }^{ 2 } }{ 12 } =1$$

Solve for x

$$x = \frac{4 \sqrt{21}}{7} \approx 2.618614683$$

$$x = -\frac{4 \sqrt{21}}{7} \approx -2.618614683$$

Steps by Finding Square Root

Multiply both sides of the equation by 48, the least common multiple of 16,12.

$$3x^{2}+4x^{2}=48$$

Combine 3x^{2} and 4x^{2} to get 7x^{2}.

$$7x^{2}=48$$

Divide both sides by 7.

$$x^{2}=\frac{48}{7}$$

Take the square root of both sides of the equation.

$$x=\frac{4\sqrt{21}}{7} x=-\frac{4\sqrt{21}}{7}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 48, the least common multiple of 16,12.

$$3x^{2}+4x^{2}=48$$

Combine 3x^{2} and 4x^{2} to get 7x^{2}.

$$7x^{2}=48$$

Subtract 48 from both sides.

$$7x^{2}-48=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, 0 for b, and -48 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 7\left(-48\right)}}{2\times 7}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 7\left(-48\right)}}{2\times 7}$$

Multiply -4 times 7.

$$x=\frac{0±\sqrt{-28\left(-48\right)}}{2\times 7}$$

Multiply -28 times -48.

$$x=\frac{0±\sqrt{1344}}{2\times 7}$$

Take the square root of 1344.

$$x=\frac{0±8\sqrt{21}}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{0±8\sqrt{21}}{14}$$

Now solve the equation x=\frac{0±8\sqrt{21}}{14} when ± is plus.

$$x=\frac{4\sqrt{21}}{7}$$

Now solve the equation x=\frac{0±8\sqrt{21}}{14} when ± is minus.

$$x=-\frac{4\sqrt{21}}{7}$$

The equation is now solved.

$$x=\frac{4\sqrt{21}}{7} x=-\frac{4\sqrt{21}}{7}$$