Solve 9(y-1)^2=16

$$9 ( y - 1 ) ^ { 2 } = 16$$

Solve for y

$$y = \frac{7}{3} = 2\frac{1}{3} \approx 2.333333333$$

$$y=-\frac{1}{3}\approx -0.333333333$$

Steps by Finding Square Root

Divide both sides by 9.

$$\frac{9\left(y-1\right)^{2}}{9}=\frac{16}{9}$$

Dividing by 9 undoes the multiplication by 9.

$$\left(y-1\right)^{2}=\frac{16}{9}$$

Take the square root of both sides of the equation.

$$y-1=\frac{4}{3} y-1=-\frac{4}{3}$$

Add 1 to both sides of the equation.

$$y-1-\left(-1\right)=\frac{4}{3}-\left(-1\right) y-1-\left(-1\right)=-\frac{4}{3}-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$y=\frac{4}{3}-\left(-1\right) y=-\frac{4}{3}-\left(-1\right)$$

Subtract -1 from \frac{4}{3}.

$$y=\frac{7}{3}$$

Subtract -1 from -\frac{4}{3}.

$$y=-\frac{1}{3}$$

The equation is now solved.

$$y=\frac{7}{3} y=-\frac{1}{3}$$