Solve 16(3-a)^2=9

$$16 ( 3 - a ) ^ { 2 } = 9$$

Solve for a

$$a = \frac{9}{4} = 2\frac{1}{4} = 2.25$$

$$a = \frac{15}{4} = 3\frac{3}{4} = 3.75$$

Steps by Finding Square Root

Divide both sides by 16.

$$\frac{16\left(-a+3\right)^{2}}{16}=\frac{9}{16}$$

Dividing by 16 undoes the multiplication by 16.

$$\left(-a+3\right)^{2}=\frac{9}{16}$$

Take the square root of both sides of the equation.

$$-a+3=\frac{3}{4} -a+3=-\frac{3}{4}$$

Subtract 3 from both sides of the equation.

$$-a+3-3=\frac{3}{4}-3 -a+3-3=-\frac{3}{4}-3$$

Subtracting 3 from itself leaves 0.

$$-a=\frac{3}{4}-3 -a=-\frac{3}{4}-3$$

Subtract 3 from \frac{3}{4}.

$$-a=-\frac{9}{4}$$

Subtract 3 from -\frac{3}{4}.

$$-a=-\frac{15}{4}$$

Divide both sides by -1.

$$\frac{-a}{-1}=-\frac{\frac{9}{4}}{-1} \frac{-a}{-1}=-\frac{\frac{15}{4}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$a=-\frac{\frac{9}{4}}{-1} a=-\frac{\frac{15}{4}}{-1}$$

Divide -\frac{9}{4} by -1.

$$a=\frac{9}{4}$$

Divide -\frac{15}{4} by -1.

$$a=\frac{15}{4}$$

The equation is now solved.

$$a=\frac{9}{4} a=\frac{15}{4}$$