Solve (7x+9)^2=5

$$( 7 x + 9 ) ^ { 2 } = 5$$

Solve for x

$$x=\frac{\sqrt{5}-9}{7}\approx -0.966276003$$

$$x=\frac{-\sqrt{5}-9}{7}\approx -1.605152568$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$7x+9=\sqrt{5} 7x+9=-\sqrt{5}$$

Subtract 9 from both sides of the equation.

$$7x+9-9=\sqrt{5}-9 7x+9-9=-\sqrt{5}-9$$

Subtracting 9 from itself leaves 0.

$$7x=\sqrt{5}-9 7x=-\sqrt{5}-9$$

Subtract 9 from \sqrt{5}.

$$7x=\sqrt{5}-9$$

Subtract 9 from -\sqrt{5}.

$$7x=-\sqrt{5}-9$$

Divide both sides by 7.

$$\frac{7x}{7}=\frac{\sqrt{5}-9}{7} \frac{7x}{7}=\frac{-\sqrt{5}-9}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$x=\frac{\sqrt{5}-9}{7} x=\frac{-\sqrt{5}-9}{7}$$