Solve each equation using the square root property. See Example 2. (x - 4)^2 = -5

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, particularly when the equation is in the form of a perfect square. It allows us to isolate the variable by taking the square root of both sides, leading to two possible solutions.

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 that yield negative values under the square root, such as in this case, complex numbers become necessary to express the solutions.

Quadratic Equations

Quadratic equations are polynomial equations of the form ax^2 + bx + c = 0, where a, b, and c are constants. Understanding the structure of quadratic equations is crucial for applying the square root property effectively, as it helps identify when the equation can be simplified to a form suitable for solving.