Question

Here are two steps from the derivation of the quadratic formula. What took place between the first step and the second step?A. Factoring a perfect square trinomial B. Completing the square C. Taking the square root of both sides

Answer 1

completing the square (option B)

Step-by-step explanation:
`x^2\text{ +}\frac{\text{ b}}{a}\text{ x = -}(c)/(a)`

Adding half the square of the coefficient of x to both sides:

`\begin{gathered} \text{coefficient of x = }\frac{\text{b}}{a} \\ \text{half the coefficient = }(b)/(2a) \\ \text{squaring half the coefficient = (}(b)/(2a))^2 \end{gathered}`
`\begin{gathered} \text{Adding the square of half the coefficient to both sides:} \\ x^2\text{ + }(b)/(a)x\text{ + (}(b)/(2a))^2\text{ = -}(c)/(a)\text{ + (}(b)/(2a))^2\text{ } \end{gathered}`

The above process is the process when applying completing the square to solve an equation.

Hence, the process that took place btween the 1st and the second step is the addition of half the square of the coeffiecient of x to both sides.

In other words, completing the square (option B)