Solve each equation using the square root property. See Example 2. 27 - x^2 = 0

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 can be rearranged into the form of a perfect square.

Rearranging Equations

Rearranging equations involves manipulating the equation to isolate the variable of interest. In the context of the given problem, we first need to move all terms to one side to set the equation to zero, which is a common practice in solving equations. This step is crucial for applying the square root property effectively.

Quadratic Equations

Quadratic equations are polynomial equations of the form ax^2 + bx + c = 0, where a, b, and c are constants. The equation in the question, 27 - x^2 = 0, can be recognized as a quadratic equation. Understanding the characteristics of quadratic equations helps in identifying appropriate methods for solving them, such as factoring, completing the square, or using the square root property.