Solve (2-3x)^2=42

$$( 2 - 3 x ) ^ { 2 } = 42$$

Solve for x

$$x=\frac{2-\sqrt{42}}{3}\approx -1.493580233$$

$$x = \frac{\sqrt{42} + 2}{3} \approx 2.826913566$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$-3x+2=\sqrt{42} -3x+2=-\sqrt{42}$$

Subtract 2 from both sides of the equation.

$$-3x+2-2=\sqrt{42}-2 -3x+2-2=-\sqrt{42}-2$$

Subtracting 2 from itself leaves 0.

$$-3x=\sqrt{42}-2 -3x=-\sqrt{42}-2$$

Subtract 2 from \sqrt{42}.

$$-3x=\sqrt{42}-2$$

Subtract 2 from -\sqrt{42}.

$$-3x=-\sqrt{42}-2$$

Divide both sides by -3.

$$\frac{-3x}{-3}=\frac{\sqrt{42}-2}{-3} \frac{-3x}{-3}=\frac{-\sqrt{42}-2}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$x=\frac{\sqrt{42}-2}{-3} x=\frac{-\sqrt{42}-2}{-3}$$

Divide \sqrt{42}-2 by -3.

$$x=\frac{2-\sqrt{42}}{3}$$

Divide -\sqrt{42}-2 by -3.

$$x=\frac{\sqrt{42}+2}{3}$$

The equation is now solved.

$$x=\frac{2-\sqrt{42}}{3} x=\frac{\sqrt{42}+2}{3}$$