Solve (4x+1)^2=3

$$( 4 x + 1 ) ^ { 2 } = 3$$

Solve for x

$$x=\frac{\sqrt{3}-1}{4}\approx 0.183012702$$

$$x=\frac{-\sqrt{3}-1}{4}\approx -0.683012702$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$4x+1=\sqrt{3} 4x+1=-\sqrt{3}$$

Subtract 1 from both sides of the equation.

$$4x+1-1=\sqrt{3}-1 4x+1-1=-\sqrt{3}-1$$

Subtracting 1 from itself leaves 0.

$$4x=\sqrt{3}-1 4x=-\sqrt{3}-1$$

Subtract 1 from \sqrt{3}.

$$4x=\sqrt{3}-1$$

Subtract 1 from -\sqrt{3}.

$$4x=-\sqrt{3}-1$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{\sqrt{3}-1}{4} \frac{4x}{4}=\frac{-\sqrt{3}-1}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{\sqrt{3}-1}{4} x=\frac{-\sqrt{3}-1}{4}$$