For Exercises 11-38, use the square root property to solve...

Key Concepts

Square Root Property

The square root property is a method used to solve equations where a variable squared equals a constant. By taking the square root of both sides of an equation of the form x² = k, you obtain x = ±?k. This property simplifies solving quadratic equations when they can be expressed in a perfect square form.

Quadratic Equations

Quadratic equations are polynomial equations of degree two. They are typically written in the form ax² + bx + c = 0. Solving these equations can involve factoring, completing the square, or using the square root property, especially when the equation can be manipulated into a form where the square root property is applicable.

Complex Numbers

Complex numbers extend the concept of the number system to include solutions of equations that do not have real solutions. When an equation involves the square root of a negative number, the solution takes the form a ± bi, where a is the real part and bi is the imaginary part, allowing for a complete set of solutions to quadratic equations.

Imaginary Unit

The imaginary unit, denoted as i, is defined by the property i² = -1. It provides a means to express the square root of negative numbers. In solving quadratic equations that result in a negative value under the square root, the imaginary unit is used to write the solutions in the standard form for complex numbers.

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