Answer: [tex]\text{x}^2\text{ + }\frac{b}{a}x\text{ + \lparen}\frac{b}{2a})\placeholder{⬚}^2\text{ = }\frac{-c}{a}\text{ + \lparen}\frac{b}{2a})\placeholder{⬚}^2\text{ \lparen2nd option\rparen}[/tex]
Explanation:
Given:
The steps to derive the quadratic formula
To find:
step 4 of the process
[tex]\begin{gathered} Step\text{ }1:\text{ }ax^2+bx+c=0 \\ Step\text{ }2:\text{ }ax^2+bx=−c \\ Step\text{ 3: x}^2\text{ + }\frac{bx}{a}\text{ = }\frac{-c}{a} \end{gathered}[/tex]
To get step 4, we will apply the complete square method. We will add the square of half the coefficient of x to both sides of the equation
coefficient of x = b/a
half the coefficient = 1/2 (b/a)
[tex]\begin{gathered} half\text{ the coefficient = }\frac{b}{2a} \\ \\ square\text{ of haalf the coefficient = \lparen}\frac{b}{2a})\placeholder{⬚}^2 \\ \\ Add\text{ to both sides:} \\ Step\text{ 4: x}^2\text{ + }\frac{b}{a}x\text{ + \lparen}\frac{b}{2a})\placeholder{⬚}^2\text{ = }\frac{-c}{a}\text{ + \lparen}\frac{b}{2a})\placeholder{⬚}^2 \end{gathered}[/tex]
