Solve (7x+23)^2=27

$$( 7 x + 23 ) ^ { 2 } = 27$$

Solve for x

$$x=\frac{3\sqrt{3}-23}{7}\approx -2.543406797$$

$$x=\frac{-3\sqrt{3}-23}{7}\approx -4.028021775$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$7x+23=3\sqrt{3} 7x+23=-3\sqrt{3}$$

Subtract 23 from both sides of the equation.

$$7x+23-23=3\sqrt{3}-23 7x+23-23=-3\sqrt{3}-23$$

Subtracting 23 from itself leaves 0.

$$7x=3\sqrt{3}-23 7x=-3\sqrt{3}-23$$

Subtract 23 from 3\sqrt{3}.

$$7x=3\sqrt{3}-23$$

Subtract 23 from -3\sqrt{3}.

$$7x=-3\sqrt{3}-23$$

Divide both sides by 7.

$$\frac{7x}{7}=\frac{3\sqrt{3}-23}{7} \frac{7x}{7}=\frac{-3\sqrt{3}-23}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$x=\frac{3\sqrt{3}-23}{7} x=\frac{-3\sqrt{3}-23}{7}$$