Solve (2y-7)^2=14

$$( 2 y - 7 ) ^ { 2 } = 14$$

Solve for y

$$y = \frac{\sqrt{14} + 7}{2} \approx 5.370828693$$

$$y = \frac{7 - \sqrt{14}}{2} \approx 1.629171307$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$2y-7=\sqrt{14} 2y-7=-\sqrt{14}$$

Add 7 to both sides of the equation.

$$2y-7-\left(-7\right)=\sqrt{14}-\left(-7\right) 2y-7-\left(-7\right)=-\sqrt{14}-\left(-7\right)$$

Subtracting -7 from itself leaves 0.

$$2y=\sqrt{14}-\left(-7\right) 2y=-\sqrt{14}-\left(-7\right)$$

Subtract -7 from \sqrt{14}.

$$2y=\sqrt{14}+7$$

Subtract -7 from -\sqrt{14}.

$$2y=7-\sqrt{14}$$

Divide both sides by 2.

$$\frac{2y}{2}=\frac{\sqrt{14}+7}{2} \frac{2y}{2}=\frac{7-\sqrt{14}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$y=\frac{\sqrt{14}+7}{2} y=\frac{7-\sqrt{14}}{2}$$