Solve 4(5-2x)^2-16=0

$$4 ( 5 - 2 x ) ^ { 2 } - 16 = 0$$

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

$$x = \frac{7}{2} = 3\frac{1}{2} = 3.5$$

Steps by Finding Square Root

Add 16 to both sides of the equation.

$$4\left(-2x+5\right)^{2}-16+16=16$$

Subtracting 16 from itself leaves 0.

$$4\left(-2x+5\right)^{2}=16$$

Divide both sides by 4.

$$\frac{4\left(-2x+5\right)^{2}}{4}=\frac{16}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$\left(-2x+5\right)^{2}=\frac{16}{4}$$

Divide 16 by 4.

$$\left(-2x+5\right)^{2}=4$$

Take the square root of both sides of the equation.

$$-2x+5=2 -2x+5=-2$$

Subtract 5 from both sides of the equation.

$$-2x+5-5=2-5 -2x+5-5=-2-5$$

Subtracting 5 from itself leaves 0.

$$-2x=2-5 -2x=-2-5$$

Subtract 5 from 2.

$$-2x=-3$$

Subtract 5 from -2.

$$-2x=-7$$

Divide both sides by -2.

$$\frac{-2x}{-2}=-\frac{3}{-2} \frac{-2x}{-2}=-\frac{7}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$x=-\frac{3}{-2} x=-\frac{7}{-2}$$

Divide -3 by -2.

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

Divide -7 by -2.

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

The equation is now solved.

$$x=\frac{3}{2} x=\frac{7}{2}$$