To convert the quadratic polynomial into the perfect square, the squared of half the value of the coefficient of degree one variable can be added to both sides of the equation. [tex]\dfrac{b^2}{4a^2}[/tex] can be added to both sides of the equation.
The given equation is [tex]x^2+\dfrac{b}{a}x+?=\dfrac{-c}{a}+?[/tex]
Now,
To change the quadratic equation into the perfect square, the squared of half the value of the coefficient of degree one variable can be added to both sides of the equation.
Therefore,
[tex]x^2+\dfrac{b}{a}x+\dfrac{b^2}{4a^2}=\dfrac{-c}{a}+\dfrac{b^2}{4a^2}[/tex]
Thus, [tex]\dfrac{b^2}{4a^2}[/tex] should be added to both sides of the equation to convert the above equation into the quadratic polynomial.
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