Solve 4z^2-44=0

$$4 z ^ { 2 } - 44 = 0$$

Solve for z

$$z=\sqrt{11}\approx 3.31662479$$

$$z=-\sqrt{11}\approx -3.31662479$$

Steps by Finding Square Root

Add 44 to both sides. Anything plus zero gives itself.

$$4z^{2}=44$$

Divide both sides by 4.

$$z^{2}=\frac{44}{4}$$

Divide 44 by 4 to get 11.

$$z^{2}=11$$

Take the square root of both sides of the equation.

$$z=\sqrt{11} z=-\sqrt{11}$$

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.

$$4z^{2}-44=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -44 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\times 4\left(-44\right)}}{2\times 4}$$

Square 0.

$$z=\frac{0±\sqrt{-4\times 4\left(-44\right)}}{2\times 4}$$

Multiply -4 times 4.

$$z=\frac{0±\sqrt{-16\left(-44\right)}}{2\times 4}$$

Multiply -16 times -44.

$$z=\frac{0±\sqrt{704}}{2\times 4}$$

Take the square root of 704.

$$z=\frac{0±8\sqrt{11}}{2\times 4}$$

Multiply 2 times 4.

$$z=\frac{0±8\sqrt{11}}{8}$$

Now solve the equation z=\frac{0±8\sqrt{11}}{8} when ± is plus.

$$z=\sqrt{11}$$

Now solve the equation z=\frac{0±8\sqrt{11}}{8} when ± is minus.

$$z=-\sqrt{11}$$

The equation is now solved.

$$z=\sqrt{11} z=-\sqrt{11}$$