Solve (9x+1)^2=14

$$( 9 x + 1 ) ^ { 2 } = 14$$

Solve for x

$$x=\frac{\sqrt{14}-1}{9}\approx 0.304628599$$

$$x=\frac{-\sqrt{14}-1}{9}\approx -0.526850821$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$9x+1=\sqrt{14} 9x+1=-\sqrt{14}$$

Subtract 1 from both sides of the equation.

$$9x+1-1=\sqrt{14}-1 9x+1-1=-\sqrt{14}-1$$

Subtracting 1 from itself leaves 0.

$$9x=\sqrt{14}-1 9x=-\sqrt{14}-1$$

Subtract 1 from \sqrt{14}.

$$9x=\sqrt{14}-1$$

Subtract 1 from -\sqrt{14}.

$$9x=-\sqrt{14}-1$$

Divide both sides by 9.

$$\frac{9x}{9}=\frac{\sqrt{14}-1}{9} \frac{9x}{9}=\frac{-\sqrt{14}-1}{9}$$

Dividing by 9 undoes the multiplication by 9.

$$x=\frac{\sqrt{14}-1}{9} x=\frac{-\sqrt{14}-1}{9}$$