Solve 3z^2-9=0

$$3 z ^ { 2 } - 9 = 0$$

Solve for z

$$z=\sqrt{3}\approx 1.732050808$$

$$z=-\sqrt{3}\approx -1.732050808$$

Steps by Finding Square Root

Add 9 to both sides. Anything plus zero gives itself.

$$3z^{2}=9$$

Divide both sides by 3.

$$z^{2}=\frac{9}{3}$$

Divide 9 by 3 to get 3.

$$z^{2}=3$$

Take the square root of both sides of the equation.

$$z=\sqrt{3} z=-\sqrt{3}$$

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.

$$3z^{2}-9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\times 3\left(-9\right)}}{2\times 3}$$

Square 0.

$$z=\frac{0±\sqrt{-4\times 3\left(-9\right)}}{2\times 3}$$

Multiply -4 times 3.

$$z=\frac{0±\sqrt{-12\left(-9\right)}}{2\times 3}$$

Multiply -12 times -9.

$$z=\frac{0±\sqrt{108}}{2\times 3}$$

Take the square root of 108.

$$z=\frac{0±6\sqrt{3}}{2\times 3}$$

Multiply 2 times 3.

$$z=\frac{0±6\sqrt{3}}{6}$$

Now solve the equation z=\frac{0±6\sqrt{3}}{6} when ± is plus.

$$z=\sqrt{3}$$

Now solve the equation z=\frac{0±6\sqrt{3}}{6} when ± is minus.

$$z=-\sqrt{3}$$

The equation is now solved.

$$z=\sqrt{3} z=-\sqrt{3}$$