The first two steps in the derivation of the quadratic formula by completing the square are:
Step 1: [tex]$a x^2+b x+c=0$[/tex]
Step 2: [tex]$a x^2+b x=-c$[/tex]
Which answer choice shows the correct next step?
A. [tex]$a x+b=\frac{-c}{x}$[/tex]
B. [tex]$a x^2+b x+\frac{b^2}{4}=-c+\frac{b^2}{4}$[/tex]
C. [tex]$x^2+\frac{b}{a} x=\frac{-c}{a}$[/tex]
D. [tex]$x^2+\frac{b}{a} x=-c$[/tex]
Answer (3)
The additive inverse of 4x is -4x
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The additive inverse of 4x is -4x, which is the value that, when added to 4x, results in zero.
The additive inverse of a term is the value that, when added to the original term, yields zero. For the expression 4x, its additive inverse is -4x. When 4x is added to -4x, the result is 0, which adheres to the general rule that a number plus its additive inverse equals zero.
This concept is a fundamental property in algebra known as inverses. Understanding additive inverses is crucial for solving equations and simplifying expressions. It is also related to the concept of distributivity, where one multiplies a sum by a factor, distributing the factor to each addend (e.g., a(b + c) = ab + ac).
The additive inverse of 4 x is − 4 x , because adding − 4 x to 4 x results in zero. Understanding additive inverses is important for solving equations in algebra. This property helps in simplifying expressions and isolating variables during calculations.
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