Solve z^2-52=0

$$z ^ { 2 } - 52 = 0$$

Solve for z

$$z=2\sqrt{13}\approx 7.211102551$$

$$z=-2\sqrt{13}\approx -7.211102551$$

Steps by Finding Square Root

Add 52 to both sides. Anything plus zero gives itself.

$$z^{2}=52$$

Take the square root of both sides of the equation.

$$z=2\sqrt{13} z=-2\sqrt{13}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$z^{2}-52=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -52 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\left(-52\right)}}{2}$$

Square 0.

$$z=\frac{0±\sqrt{-4\left(-52\right)}}{2}$$

Multiply -4 times -52.

$$z=\frac{0±\sqrt{208}}{2}$$

Take the square root of 208.

$$z=\frac{0±4\sqrt{13}}{2}$$

Now solve the equation z=\frac{0±4\sqrt{13}}{2} when ± is plus.

$$z=2\sqrt{13}$$

Now solve the equation z=\frac{0±4\sqrt{13}}{2} when ± is minus.

$$z=-2\sqrt{13}$$

The equation is now solved.

$$z=2\sqrt{13} z=-2\sqrt{13}$$