Solve x^2-4=-76

$$x ^ { 2 } - 4 = - 76$$

Solve for x (complex solution)

$$x=-6\sqrt{2}i\approx -0-8.485281374i$$

$$x=6\sqrt{2}i\approx 8.485281374i$$

Steps by Finding Square Root

Add 4 to both sides.

$$x^{2}=-76+4$$

Add -76 and 4 to get -72.

$$x^{2}=-72$$

The equation is now solved.

$$x=6\sqrt{2}i x=-6\sqrt{2}i$$

Steps Using the Quadratic Formula

Add 76 to both sides.

$$x^{2}-4+76=0$$

Add -4 and 76 to get 72.

$$x^{2}+72=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 72 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 72}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 72}}{2}$$

Multiply -4 times 72.

$$x=\frac{0±\sqrt{-288}}{2}$$

Take the square root of -288.

$$x=\frac{0±12\sqrt{2}i}{2}$$

Now solve the equation x=\frac{0±12\sqrt{2}i}{2} when ± is plus.

$$x=6\sqrt{2}i$$

Now solve the equation x=\frac{0±12\sqrt{2}i}{2} when ± is minus.

$$x=-6\sqrt{2}i$$

The equation is now solved.

$$x=6\sqrt{2}i x=-6\sqrt{2}i$$