Solve (9x-5)^2-4=0

$$( 9 x - 5 ) ^ { 2 } - 4 = 0$$

Solve for x

$$x=\frac{7}{9}\approx 0.777777778$$

$$x=\frac{1}{3}\approx 0.333333333$$

Steps by Finding Square Root

Add 4 to both sides of the equation.

$$\left(9x-5\right)^{2}-4+4=4$$

Subtracting 4 from itself leaves 0.

$$\left(9x-5\right)^{2}=4$$

Take the square root of both sides of the equation.

$$9x-5=2 9x-5=-2$$

Add 5 to both sides of the equation.

$$9x-5-\left(-5\right)=2-\left(-5\right) 9x-5-\left(-5\right)=-2-\left(-5\right)$$

Subtracting -5 from itself leaves 0.

$$9x=2-\left(-5\right) 9x=-2-\left(-5\right)$$

Subtract -5 from 2.

$$9x=7$$

Subtract -5 from -2.

$$9x=3$$

Divide both sides by 9.

$$\frac{9x}{9}=\frac{7}{9} \frac{9x}{9}=\frac{3}{9}$$

Dividing by 9 undoes the multiplication by 9.

$$x=\frac{7}{9} x=\frac{3}{9}$$

Divide 7 by 9.

$$x=\frac{7}{9}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

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

The equation is now solved.

$$x=\frac{7}{9} x=\frac{1}{3}$$