Solve (5x-7)^2=12

$$( 5 x - 7 ) ^ { 2 } = 12$$

Solve for x

$$x = \frac{2 \sqrt{3} + 7}{5} \approx 2.092820323$$

$$x=\frac{7-2\sqrt{3}}{5}\approx 0.707179677$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$5x-7=2\sqrt{3} 5x-7=-2\sqrt{3}$$

Add 7 to both sides of the equation.

$$5x-7-\left(-7\right)=2\sqrt{3}-\left(-7\right) 5x-7-\left(-7\right)=-2\sqrt{3}-\left(-7\right)$$

Subtracting -7 from itself leaves 0.

$$5x=2\sqrt{3}-\left(-7\right) 5x=-2\sqrt{3}-\left(-7\right)$$

Subtract -7 from 2\sqrt{3}.

$$5x=2\sqrt{3}+7$$

Subtract -7 from -2\sqrt{3}.

$$5x=7-2\sqrt{3}$$

Divide both sides by 5.

$$\frac{5x}{5}=\frac{2\sqrt{3}+7}{5} \frac{5x}{5}=\frac{7-2\sqrt{3}}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$x=\frac{2\sqrt{3}+7}{5} x=\frac{7-2\sqrt{3}}{5}$$