Solve 52-(j-1)^2=32

$$52 - ( j - 1 ) ^ { 2 } = 32$$

Solve for j

$$j=2\sqrt{5}+1\approx 5.472135955$$

$$j=1-2\sqrt{5}\approx -3.472135955$$

Steps by Finding Square Root

Subtract 52 from both sides of the equation.

$$-\left(j-1\right)^{2}+52-52=32-52$$

Subtracting 52 from itself leaves 0.

$$-\left(j-1\right)^{2}=32-52$$

Subtract 52 from 32.

$$-\left(j-1\right)^{2}=-20$$

Divide both sides by -1.

$$\frac{-\left(j-1\right)^{2}}{-1}=-\frac{20}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$\left(j-1\right)^{2}=-\frac{20}{-1}$$

Divide -20 by -1.

$$\left(j-1\right)^{2}=20$$

Take the square root of both sides of the equation.

$$j-1=2\sqrt{5} j-1=-2\sqrt{5}$$

Add 1 to both sides of the equation.

$$j-1-\left(-1\right)=2\sqrt{5}-\left(-1\right) j-1-\left(-1\right)=-2\sqrt{5}-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$j=2\sqrt{5}-\left(-1\right) j=-2\sqrt{5}-\left(-1\right)$$

Subtract -1 from 2\sqrt{5}.

$$j=2\sqrt{5}+1$$

Subtract -1 from -2\sqrt{5}.

$$j=1-2\sqrt{5}$$

The equation is now solved.

$$j=2\sqrt{5}+1 j=1-2\sqrt{5}$$