Solve (1/2x)^2=4

$$( \frac { 1 } { 2 } x ) ^ { 2 } = 4$$

Solve for x

$$x=4$$

$$x=-4$$

Steps Using Difference of Squares

Expand \left(\frac{1}{2}x\right)^{2}.

$$\left(\frac{1}{2}\right)^{2}x^{2}=4$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{1}{4}x^{2}=4$$

Subtract 4 from both sides.

$$\frac{1}{4}x^{2}-4=0$$

Multiply both sides by 4.

$$x^{2}-16=0$$

Consider x^{2}-16. Rewrite x^{2}-16 as x^{2}-4^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-4\right)\left(x+4\right)=0$$

To find equation solutions, solve x-4=0 and x+4=0.

$$x=4 x=-4$$

Steps by Finding Square Root

Expand \left(\frac{1}{2}x\right)^{2}.

$$\left(\frac{1}{2}\right)^{2}x^{2}=4$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{1}{4}x^{2}=4$$

Multiply both sides by 4, the reciprocal of \frac{1}{4}.

$$x^{2}=4\times 4$$

Multiply 4 and 4 to get 16.

$$x^{2}=16$$

Take the square root of both sides of the equation.

$$x=4 x=-4$$

Steps Using the Quadratic Formula

Expand \left(\frac{1}{2}x\right)^{2}.

$$\left(\frac{1}{2}\right)^{2}x^{2}=4$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{1}{4}x^{2}=4$$

Subtract 4 from both sides.

$$\frac{1}{4}x^{2}-4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1}{4} for a, 0 for b, and -4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{4}\left(-4\right)}}{2\times \frac{1}{4}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{1}{4}\left(-4\right)}}{2\times \frac{1}{4}}$$

Multiply -4 times \frac{1}{4}.

$$x=\frac{0±\sqrt{-\left(-4\right)}}{2\times \frac{1}{4}}$$

Multiply -1 times -4.

$$x=\frac{0±\sqrt{4}}{2\times \frac{1}{4}}$$

Take the square root of 4.

$$x=\frac{0±2}{2\times \frac{1}{4}}$$

Multiply 2 times \frac{1}{4}.

$$x=\frac{0±2}{\frac{1}{2}}$$

Now solve the equation x=\frac{0±2}{\frac{1}{2}} when ± is plus. Divide 2 by \frac{1}{2} by multiplying 2 by the reciprocal of \frac{1}{2}.

$$x=4$$

Now solve the equation x=\frac{0±2}{\frac{1}{2}} when ± is minus. Divide -2 by \frac{1}{2} by multiplying -2 by the reciprocal of \frac{1}{2}.

$$x=-4$$

The equation is now solved.

$$x=4 x=-4$$