Solve 3z^2-27=0

$$3 z ^ { 2 } - 27 = 0$$

Solve for z

$$z=3$$

$$z=-3$$

Steps Using Difference of Squares

Divide both sides by 3.

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

Consider z^{2}-9. Rewrite z^{2}-9 as z^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(z-3\right)\left(z+3\right)=0$$

To find equation solutions, solve z-3=0 and z+3=0.

$$z=3 z=-3$$

Steps by Finding Square Root

Add 27 to both sides. Anything plus zero gives itself.

$$3z^{2}=27$$

Divide both sides by 3.

$$z^{2}=\frac{27}{3}$$

Divide 27 by 3 to get 9.

$$z^{2}=9$$

Take the square root of both sides of the equation.

$$z=3 z=-3$$

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.

$$3z^{2}-27=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -27 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\times 3\left(-27\right)}}{2\times 3}$$

Square 0.

$$z=\frac{0±\sqrt{-4\times 3\left(-27\right)}}{2\times 3}$$

Multiply -4 times 3.

$$z=\frac{0±\sqrt{-12\left(-27\right)}}{2\times 3}$$

Multiply -12 times -27.

$$z=\frac{0±\sqrt{324}}{2\times 3}$$

Take the square root of 324.

$$z=\frac{0±18}{2\times 3}$$

Multiply 2 times 3.

$$z=\frac{0±18}{6}$$

Now solve the equation z=\frac{0±18}{6} when ± is plus. Divide 18 by 6.

$$z=3$$

Now solve the equation z=\frac{0±18}{6} when ± is minus. Divide -18 by 6.

$$z=-3$$

The equation is now solved.

$$z=3 z=-3$$