Find all real and complex solutions of the quadratic equation $(x+7{)}^2+28=0$ .

A) $4\pm 7\sqrt{7}$
B) $7\pm 2\sqrt{7}$
C) $7\pm 4\sqrt{7}i$
D) $-2\pm 7\sqrt{7}i$
E) $-7\pm 2\sqrt{7}i$

Complex Solutions

Solutions to an equation that include imaginary numbers, indicating they cannot be plotted on the standard real number line.

Real Solutions

Solutions to an equation that do not involve imaginary or complex numbers, and can be plotted on a real number line.

Quadratic Equation

A quadratic equation is a second-degree polynomial equation, typically in the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.