Solve (y-5)^2-32=0

$$( y - 5 ) ^ { 2 } - 32 = 0$$

Solve for y

$$y=4\sqrt{2}+5\approx 10.656854249$$

$$y=5-4\sqrt{2}\approx -0.656854249$$

Steps by Finding Square Root

Add 32 to both sides of the equation.

$$\left(y-5\right)^{2}-32+32=32$$

Subtracting 32 from itself leaves 0.

$$\left(y-5\right)^{2}=32$$

Take the square root of both sides of the equation.

$$y-5=4\sqrt{2} y-5=-4\sqrt{2}$$

Add 5 to both sides of the equation.

$$y-5-\left(-5\right)=4\sqrt{2}-\left(-5\right) y-5-\left(-5\right)=-4\sqrt{2}-\left(-5\right)$$

Subtracting -5 from itself leaves 0.

$$y=4\sqrt{2}-\left(-5\right) y=-4\sqrt{2}-\left(-5\right)$$

Subtract -5 from 4\sqrt{2}.

$$y=4\sqrt{2}+5$$

Subtract -5 from -4\sqrt{2}.

$$y=5-4\sqrt{2}$$

The equation is now solved.

$$y=4\sqrt{2}+5 y=5-4\sqrt{2}$$