Solve -36z^2-5=0

$$- 36 z ^ { 2 } - 5 = 0$$

Solve for z

$$z=-\frac{\sqrt{5}i}{6}\approx -0-0.372677996i$$

$$z=\frac{\sqrt{5}i}{6}\approx 0.372677996i$$

Steps by Finding Square Root

Add 5 to both sides. Anything plus zero gives itself.

$$-36z^{2}=5$$

Divide both sides by -36.

$$z^{2}=-\frac{5}{36}$$

The equation is now solved.

$$z=\frac{\sqrt{5}i}{6} z=-\frac{\sqrt{5}i}{6}$$

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.

$$-36z^{2}-5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -36 for a, 0 for b, and -5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\left(-36\right)\left(-5\right)}}{2\left(-36\right)}$$

Square 0.

$$z=\frac{0±\sqrt{-4\left(-36\right)\left(-5\right)}}{2\left(-36\right)}$$

Multiply -4 times -36.

$$z=\frac{0±\sqrt{144\left(-5\right)}}{2\left(-36\right)}$$

Multiply 144 times -5.

$$z=\frac{0±\sqrt{-720}}{2\left(-36\right)}$$

Take the square root of -720.

$$z=\frac{0±12\sqrt{5}i}{2\left(-36\right)}$$

Multiply 2 times -36.

$$z=\frac{0±12\sqrt{5}i}{-72}$$

Now solve the equation z=\frac{0±12\sqrt{5}i}{-72} when ± is plus.

$$z=-\frac{\sqrt{5}i}{6}$$

Now solve the equation z=\frac{0±12\sqrt{5}i}{-72} when ± is minus.

$$z=\frac{\sqrt{5}i}{6}$$

The equation is now solved.

$$z=-\frac{\sqrt{5}i}{6} z=\frac{\sqrt{5}i}{6}$$