Solve z^2+4-43-36=0

$$z ^ { 2 } + 4 - 43 - 36 = 0$$

Solve for z

$$z=5\sqrt{3}\approx 8.660254038$$

$$z=-5\sqrt{3}\approx -8.660254038$$

Steps by Finding Square Root

Subtract 43 from 4 to get -39.

$$z^{2}-39-36=0$$

Subtract 36 from -39 to get -75.

$$z^{2}-75=0$$

Add 75 to both sides. Anything plus zero gives itself.

$$z^{2}=75$$

Take the square root of both sides of the equation.

$$z=5\sqrt{3} z=-5\sqrt{3}$$

Steps Using the Quadratic Formula

Subtract 43 from 4 to get -39.

$$z^{2}-39-36=0$$

Subtract 36 from -39 to get -75.

$$z^{2}-75=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -75 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\left(-75\right)}}{2}$$

Square 0.

$$z=\frac{0±\sqrt{-4\left(-75\right)}}{2}$$

Multiply -4 times -75.

$$z=\frac{0±\sqrt{300}}{2}$$

Take the square root of 300.

$$z=\frac{0±10\sqrt{3}}{2}$$

Now solve the equation z=\frac{0±10\sqrt{3}}{2} when ± is plus.

$$z=5\sqrt{3}$$

Now solve the equation z=\frac{0±10\sqrt{3}}{2} when ± is minus.

$$z=-5\sqrt{3}$$

The equation is now solved.

$$z=5\sqrt{3} z=-5\sqrt{3}$$