Solve 96-2z^2-4z^2=0

$$96 - 2 z ^ { 2 } - 4 z ^ { 2 } = 0$$

Solve for z

$$z=4$$

$$z=-4$$

Steps by Finding Square Root

Combine -2z^{2} and -4z^{2} to get -6z^{2}.

$$96-6z^{2}=0$$

Subtract 96 from both sides. Anything subtracted from zero gives its negation.

$$-6z^{2}=-96$$

Divide both sides by -6.

$$z^{2}=\frac{-96}{-6}$$

Divide -96 by -6 to get 16.

$$z^{2}=16$$

Take the square root of both sides of the equation.

$$z=4 z=-4$$

Steps Using the Quadratic Formula

Combine -2z^{2} and -4z^{2} to get -6z^{2}.

$$96-6z^{2}=0$$

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.

$$-6z^{2}+96=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -6 for a, 0 for b, and 96 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\left(-6\right)\times 96}}{2\left(-6\right)}$$

Square 0.

$$z=\frac{0±\sqrt{-4\left(-6\right)\times 96}}{2\left(-6\right)}$$

Multiply -4 times -6.

$$z=\frac{0±\sqrt{24\times 96}}{2\left(-6\right)}$$

Multiply 24 times 96.

$$z=\frac{0±\sqrt{2304}}{2\left(-6\right)}$$

Take the square root of 2304.

$$z=\frac{0±48}{2\left(-6\right)}$$

Multiply 2 times -6.

$$z=\frac{0±48}{-12}$$

Now solve the equation z=\frac{0±48}{-12} when ± is plus. Divide 48 by -12.

$$z=-4$$

Now solve the equation z=\frac{0±48}{-12} when ± is minus. Divide -48 by -12.

$$z=4$$

The equation is now solved.

$$z=-4 z=4$$