Use Choices A–D to answer each question. A. 3x^2 - 17x - 6 = 0 B. (2x + 5)^2 = 7 C. x^2 + x = 12 D. (3x - 1)(x - 7) = 0 Only one of the equations does not require Step 1 of the method for completing the square described in this section. Which one is it? Solve it.

Key Concepts

Completing the Square

Completing the square is a method used to solve quadratic equations by transforming them into a perfect square trinomial. This involves rearranging the equation and adding a specific value to both sides to create a binomial squared. This technique is particularly useful for deriving the quadratic formula and analyzing the properties of quadratic functions.

Quadratic Equations

A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and a ≠ 0. The solutions to these equations can be found using various methods, including factoring, completing the square, or applying the quadratic formula. Understanding the structure of quadratic equations is essential for identifying the appropriate solving method.

Factoring

Factoring is the process of breaking down an expression into a product of simpler expressions, which can make solving equations easier. For quadratic equations, this often involves finding two binomials that multiply to give the original quadratic. Recognizing when an equation can be factored directly can save time and simplify the solving process.