Answer:
[tex]\huge\boxed{\sf Option \ B}[/tex]
Step-by-step explanation:
[tex]\displaystyle x^2+\frac{bx}{a} =\frac{-c}{a}[/tex] --------------------(1)
Take the expression
[tex]\displaystyle x^2 + \frac{bx}{a}[/tex]
We can also write it as:
[tex]\displaystyle (x)^2 + 2(x)(\frac{b}{2a} )[/tex]
According to the formula [tex]a^2+2ab+b^2[/tex], the b of this expression is [tex]\displaystyle \frac{b}{2a}[/tex]. So,
b² will be:
[tex]\displaystyle =(\frac{b}{2a} )^2\\\\=\frac{b^2}{4a^2}[/tex]
So, we will add [tex]\displaystyle \frac{b^2}{4a^2}[/tex] to both sides in Eq. (1)
For STEP 4, the equation will become:
[tex]\displaystyle x^2+\frac{bx}{a} + \frac{b^2}{4a^2} = \frac{-c}{a} + \frac{b^2}{4a^2}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Answer:
Below in bold.
Step-by-step explanation:
The next step is to divide b/a by 2 then square it and add to both sides.
This creates a perfect square quadratic on left side.
So the answer is :
x squared plus b over a times x plus quantity b over 2 times a all squared equals negative c over a plus quantity b over 2 times a all squared
