Solve 9(3x+1)^2=64

$$9 ( 3 x + 1 ) ^ { 2 } = 64$$

Solve for x

$$x=\frac{5}{9}\approx 0.555555556$$

$$x = -\frac{11}{9} = -1\frac{2}{9} \approx -1.222222222$$

Steps by Finding Square Root

Divide both sides by 9.

$$\frac{9\left(3x+1\right)^{2}}{9}=\frac{64}{9}$$

Dividing by 9 undoes the multiplication by 9.

$$\left(3x+1\right)^{2}=\frac{64}{9}$$

Take the square root of both sides of the equation.

$$3x+1=\frac{8}{3} 3x+1=-\frac{8}{3}$$

Subtract 1 from both sides of the equation.

$$3x+1-1=\frac{8}{3}-1 3x+1-1=-\frac{8}{3}-1$$

Subtracting 1 from itself leaves 0.

$$3x=\frac{8}{3}-1 3x=-\frac{8}{3}-1$$

Subtract 1 from \frac{8}{3}.

$$3x=\frac{5}{3}$$

Subtract 1 from -\frac{8}{3}.

$$3x=-\frac{11}{3}$$

Divide both sides by 3.

$$\frac{3x}{3}=\frac{\frac{5}{3}}{3} \frac{3x}{3}=-\frac{\frac{11}{3}}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x=\frac{\frac{5}{3}}{3} x=-\frac{\frac{11}{3}}{3}$$

Divide \frac{5}{3} by 3.

$$x=\frac{5}{9}$$

Divide -\frac{11}{3} by 3.

$$x=-\frac{11}{9}$$

The equation is now solved.

$$x=\frac{5}{9} x=-\frac{11}{9}$$