Solve each equation using the square root property. See Example 2. x^2 = -400

Key Concepts

Square Root Property

The square root property states that if x^2 = k, then x = ±√k. This property is essential for solving quadratic equations, as it allows us to isolate the variable by taking the square root of both sides. It is particularly useful when the equation is already in the form of a perfect square.

Complex Numbers

Complex numbers are numbers that have a real part and an imaginary part, expressed in the form a + bi, where i is the imaginary unit defined as √(-1). When solving equations like x^2 = -400, the square root of a negative number leads to complex solutions, which are crucial for understanding the complete set of solutions in algebra.

Quadratic Equations

Quadratic equations are polynomial equations of the form ax^2 + bx + c = 0, where a, b, and c are constants. They can have zero, one, or two real or complex solutions. Understanding the nature of these equations and their solutions is fundamental in algebra, especially when applying methods like the square root property.