Solve (2-a)^2-9=-135/16

$$( 2 - a ) ^ { 2 } - 9 = - \frac { 135 } { 16 }$$

Solve for a

$$a = \frac{5}{4} = 1\frac{1}{4} = 1.25$$

$$a = \frac{11}{4} = 2\frac{3}{4} = 2.75$$

Steps by Finding Square Root

Add 9 to both sides of the equation.

$$\left(-a+2\right)^{2}-9+9=-\frac{135}{16}+9$$

Subtracting 9 from itself leaves 0.

$$\left(-a+2\right)^{2}=-\frac{135}{16}+9$$

Add -\frac{135}{16} to 9.

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

Take the square root of both sides of the equation.

$$-a+2=\frac{3}{4} -a+2=-\frac{3}{4}$$

Subtract 2 from both sides of the equation.

$$-a+2-2=\frac{3}{4}-2 -a+2-2=-\frac{3}{4}-2$$

Subtracting 2 from itself leaves 0.

$$-a=\frac{3}{4}-2 -a=-\frac{3}{4}-2$$

Subtract 2 from \frac{3}{4}.

$$-a=-\frac{5}{4}$$

Subtract 2 from -\frac{3}{4}.

$$-a=-\frac{11}{4}$$

Divide both sides by -1.

$$\frac{-a}{-1}=-\frac{\frac{5}{4}}{-1} \frac{-a}{-1}=-\frac{\frac{11}{4}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$a=-\frac{\frac{5}{4}}{-1} a=-\frac{\frac{11}{4}}{-1}$$

Divide -\frac{5}{4} by -1.

$$a=\frac{5}{4}$$

Divide -\frac{11}{4} by -1.

$$a=\frac{11}{4}$$

The equation is now solved.

$$a=\frac{5}{4} a=\frac{11}{4}$$