Solve 4^2+x^2=(x/2)^2

$$4 ^ { 2 } + x ^ { 2 } = ( \frac { x } { 2 } ) ^ { 2 }$$

Solve for x (complex solution)

$$x=-\frac{8\sqrt{3}i}{3}\approx -0-4.618802154i$$

$$x=\frac{8\sqrt{3}i}{3}\approx 4.618802154i$$

Steps by Finding Square Root

Calculate 4 to the power of 2 and get 16.

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

To raise \frac{x}{2} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 2 to the power of 2 and get 4.

$$16+x^{2}=\frac{x^{2}}{4}$$

Subtract \frac{x^{2}}{4} from both sides.

$$16+x^{2}-\frac{x^{2}}{4}=0$$

Combine x^{2} and -\frac{x^{2}}{4} to get \frac{3}{4}x^{2}.

$$16+\frac{3}{4}x^{2}=0$$

Subtract 16 from both sides. Anything subtracted from zero gives its negation.

$$\frac{3}{4}x^{2}=-16$$

Multiply both sides by \frac{4}{3}, the reciprocal of \frac{3}{4}.

$$x^{2}=-16\times \frac{4}{3}$$

Multiply -16 and \frac{4}{3} to get -\frac{64}{3}.

$$x^{2}=-\frac{64}{3}$$

The equation is now solved.

$$x=\frac{8\sqrt{3}i}{3} x=-\frac{8\sqrt{3}i}{3}$$

Steps Using the Quadratic Formula

Calculate 4 to the power of 2 and get 16.

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

To raise \frac{x}{2} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 2 to the power of 2 and get 4.

$$16+x^{2}=\frac{x^{2}}{4}$$

Subtract \frac{x^{2}}{4} from both sides.

$$16+x^{2}-\frac{x^{2}}{4}=0$$

Combine x^{2} and -\frac{x^{2}}{4} to get \frac{3}{4}x^{2}.

$$16+\frac{3}{4}x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$\frac{3}{4}x^{2}+16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{3}{4} for a, 0 for b, and 16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{3}{4}\times 16}}{2\times \frac{3}{4}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{3}{4}\times 16}}{2\times \frac{3}{4}}$$

Multiply -4 times \frac{3}{4}.

$$x=\frac{0±\sqrt{-3\times 16}}{2\times \frac{3}{4}}$$

Multiply -3 times 16.

$$x=\frac{0±\sqrt{-48}}{2\times \frac{3}{4}}$$

Take the square root of -48.

$$x=\frac{0±4\sqrt{3}i}{2\times \frac{3}{4}}$$

Multiply 2 times \frac{3}{4}.

$$x=\frac{0±4\sqrt{3}i}{\frac{3}{2}}$$

Now solve the equation x=\frac{0±4\sqrt{3}i}{\frac{3}{2}} when ± is plus.

$$x=\frac{8\sqrt{3}i}{3}$$

Now solve the equation x=\frac{0±4\sqrt{3}i}{\frac{3}{2}} when ± is minus.

$$x=-\frac{8\sqrt{3}i}{3}$$

The equation is now solved.

$$x=\frac{8\sqrt{3}i}{3} x=-\frac{8\sqrt{3}i}{3}$$