Solve x^2+72-3=21

$$x ^ { 2 } + 72 - 3 = 21$$

Solve for x (complex solution)

$$x=-4\sqrt{3}i\approx -0-6.92820323i$$

$$x=4\sqrt{3}i\approx 6.92820323i$$

Steps by Finding Square Root

Subtract 3 from 72 to get 69.

$$x^{2}+69=21$$

Subtract 69 from both sides.

$$x^{2}=21-69$$

Subtract 69 from 21 to get -48.

$$x^{2}=-48$$

The equation is now solved.

$$x=4\sqrt{3}i x=-4\sqrt{3}i$$

Steps Using the Quadratic Formula

Subtract 3 from 72 to get 69.

$$x^{2}+69=21$$

Subtract 21 from both sides.

$$x^{2}+69-21=0$$

Subtract 21 from 69 to get 48.

$$x^{2}+48=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 48 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 48}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 48}}{2}$$

Multiply -4 times 48.

$$x=\frac{0±\sqrt{-192}}{2}$$

Take the square root of -192.

$$x=\frac{0±8\sqrt{3}i}{2}$$

Now solve the equation x=\frac{0±8\sqrt{3}i}{2} when ± is plus.

$$x=4\sqrt{3}i$$

Now solve the equation x=\frac{0±8\sqrt{3}i}{2} when ± is minus.

$$x=-4\sqrt{3}i$$

The equation is now solved.

$$x=4\sqrt{3}i x=-4\sqrt{3}i$$