Question

The method of solving a quadratic equation best used when the

coefficient of the x term is even and the leading coefficient is one
A) Completing the Square
B) Using Square Root Method
C) Quadratic Formula
D) Graphing

Answer 1

The method of solving quadratic equations with even x coefficient and leading coefficient one is completing the square.

Step-by-step explanation:

The method of solving quadratic equations when the coefficient of the x term is even and the leading coefficient is one is Completing the Square. This method involves transforming the equation into a perfect square trinomial and then solving for x. Here's an example:

Let's say we have the equation 2x^2 + 4x - 6 = 0.

To complete the square, we divide each term by the coefficient of x^2 to make it equal to 1: x^2 + 2x - 3 = 0.

Next, we take half the coefficient of x (2 in this case), square it (2^2 = 4), and add it to both sides of the equation: x^2 + 2x + 4 - 3 - 4 = 0.

The left side of the equation can be written as (x + 1)^2 - 7 = 0. Solving further gives us (x + 1)^2 = 7, and taking the square root of both sides, we get x + 1 = ±√7. Finally, subtract 1 from both sides to find the solutions, x = -1 ± √7.