Solve (4/5x-1)^2=4/9

$$( \frac { 4 } { 5 } x - 1 ) ^ { 2 } = \frac { 4 } { 9 }$$

Solve for x

$$x = \frac{25}{12} = 2\frac{1}{12} \approx 2.083333333$$

$$x=\frac{5}{12}\approx 0.416666667$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$\frac{4}{5}x-1=\frac{2}{3} \frac{4}{5}x-1=-\frac{2}{3}$$

Add 1 to both sides of the equation.

$$\frac{4}{5}x-1-\left(-1\right)=\frac{2}{3}-\left(-1\right) \frac{4}{5}x-1-\left(-1\right)=-\frac{2}{3}-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$\frac{4}{5}x=\frac{2}{3}-\left(-1\right) \frac{4}{5}x=-\frac{2}{3}-\left(-1\right)$$

Subtract -1 from \frac{2}{3}.

$$\frac{4}{5}x=\frac{5}{3}$$

Subtract -1 from -\frac{2}{3}.

$$\frac{4}{5}x=\frac{1}{3}$$

Divide both sides of the equation by \frac{4}{5}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{4}{5}x}{\frac{4}{5}}=\frac{\frac{5}{3}}{\frac{4}{5}} \frac{\frac{4}{5}x}{\frac{4}{5}}=\frac{\frac{1}{3}}{\frac{4}{5}}$$

Dividing by \frac{4}{5} undoes the multiplication by \frac{4}{5}.

$$x=\frac{\frac{5}{3}}{\frac{4}{5}} x=\frac{\frac{1}{3}}{\frac{4}{5}}$$

Divide \frac{5}{3} by \frac{4}{5} by multiplying \frac{5}{3} by the reciprocal of \frac{4}{5}.

$$x=\frac{25}{12}$$

Divide \frac{1}{3} by \frac{4}{5} by multiplying \frac{1}{3} by the reciprocal of \frac{4}{5}.

$$x=\frac{5}{12}$$

The equation is now solved.

$$x=\frac{25}{12} x=\frac{5}{12}$$