Solve (6x-5)^2=50

$$( 6 x - 5 ) ^ { 2 } = 50$$

Solve for x

$$x = \frac{5 \sqrt{2} + 5}{6} \approx 2.011844635$$

$$x=\frac{5-5\sqrt{2}}{6}\approx -0.345177969$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$6x-5=5\sqrt{2} 6x-5=-5\sqrt{2}$$

Add 5 to both sides of the equation.

$$6x-5-\left(-5\right)=5\sqrt{2}-\left(-5\right) 6x-5-\left(-5\right)=-5\sqrt{2}-\left(-5\right)$$

Subtracting -5 from itself leaves 0.

$$6x=5\sqrt{2}-\left(-5\right) 6x=-5\sqrt{2}-\left(-5\right)$$

Subtract -5 from 5\sqrt{2}.

$$6x=5\sqrt{2}+5$$

Subtract -5 from -5\sqrt{2}.

$$6x=5-5\sqrt{2}$$

Divide both sides by 6.

$$\frac{6x}{6}=\frac{5\sqrt{2}+5}{6} \frac{6x}{6}=\frac{5-5\sqrt{2}}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$x=\frac{5\sqrt{2}+5}{6} x=\frac{5-5\sqrt{2}}{6}$$