Solve 5^2-z^2=3^2+x

$$5 ^ { 2 } - z ^ { 2 } = 3 ^ { 2 } + x$$

Solve for x

$$x=16-z^{2}$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$25-z^{2}=3^{2}+x$$

Calculate 3 to the power of 2 and get 9.

$$25-z^{2}=9+x$$

Swap sides so that all variable terms are on the left hand side.

$$9+x=25-z^{2}$$

Subtract 9 from both sides.

$$x=25-z^{2}-9$$

Subtract 9 from 25 to get 16.

$$x=16-z^{2}$$

Solve for z (complex solution)

$$z=-\sqrt{16-x}$$

$$z=\sqrt{16-x}$$

Solve for z

$$z=\sqrt{16-x}$$

$$z=-\sqrt{16-x}\text{, }x\leq 16$$