Solve x^2+4(1-x^2/16)=12

$$x ^ { 2 } + 4 ( 1 - \frac { x ^ { 2 } } { 16 } ) = 12$$

Solve for x

$$x = \frac{4 \sqrt{6}}{3} \approx 3.265986324$$

$$x = -\frac{4 \sqrt{6}}{3} \approx -3.265986324$$

Steps by Finding Square Root

Multiply both sides of the equation by 16.

$$16x^{2}+64\left(1-\frac{x^{2}}{16}\right)=192$$

Use the distributive property to multiply 64 by 1-\frac{x^{2}}{16}.

$$16x^{2}+64+64\left(-\frac{x^{2}}{16}\right)=192$$

Cancel out 16, the greatest common factor in 64 and 16.

$$16x^{2}+64-4x^{2}=192$$

Combine 16x^{2} and -4x^{2} to get 12x^{2}.

$$12x^{2}+64=192$$

Subtract 64 from both sides.

$$12x^{2}=192-64$$

Subtract 64 from 192 to get 128.

$$12x^{2}=128$$

Divide both sides by 12.

$$x^{2}=\frac{128}{12}$$

Reduce the fraction \frac{128}{12} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{32}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{4\sqrt{6}}{3} x=-\frac{4\sqrt{6}}{3}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 16.

$$16x^{2}+64\left(1-\frac{x^{2}}{16}\right)=192$$

Use the distributive property to multiply 64 by 1-\frac{x^{2}}{16}.

$$16x^{2}+64+64\left(-\frac{x^{2}}{16}\right)=192$$

Cancel out 16, the greatest common factor in 64 and 16.

$$16x^{2}+64-4x^{2}=192$$

Combine 16x^{2} and -4x^{2} to get 12x^{2}.

$$12x^{2}+64=192$$

Subtract 192 from both sides.

$$12x^{2}+64-192=0$$

Subtract 192 from 64 to get -128.

$$12x^{2}-128=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 12 for a, 0 for b, and -128 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 12\left(-128\right)}}{2\times 12}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 12\left(-128\right)}}{2\times 12}$$

Multiply -4 times 12.

$$x=\frac{0±\sqrt{-48\left(-128\right)}}{2\times 12}$$

Multiply -48 times -128.

$$x=\frac{0±\sqrt{6144}}{2\times 12}$$

Take the square root of 6144.

$$x=\frac{0±32\sqrt{6}}{2\times 12}$$

Multiply 2 times 12.

$$x=\frac{0±32\sqrt{6}}{24}$$

Now solve the equation x=\frac{0±32\sqrt{6}}{24} when ± is plus.

$$x=\frac{4\sqrt{6}}{3}$$

Now solve the equation x=\frac{0±32\sqrt{6}}{24} when ± is minus.

$$x=-\frac{4\sqrt{6}}{3}$$

The equation is now solved.

$$x=\frac{4\sqrt{6}}{3} x=-\frac{4\sqrt{6}}{3}$$