Alright, let's go through the steps to solve this expression:
Given the expression:
[tex]\[ +21.80 - 20c + 29.80 - 20c + 12 \][/tex]
Our goal is to simplify this expression and then match it with the form:
[tex]\[ -\square + 20c \][/tex]
1. Combine like terms on the left side:
- First, let's collect all the constants:
[tex]\[
21.80 + 29.80 + 12
\][/tex]
- Then combine the constants:
[tex]\[
21.80 + 29.80 = 51.60
\][/tex]
[tex]\[
51.60 + 12 = 63.60
\][/tex]
- Next, we combine the [tex]\(-20c\)[/tex] terms:
[tex]\[
-20c - 20c = -40c
\][/tex]
- Putting it all together, we combine the constants with the variable term:
[tex]\[
63.60 - 40c
\][/tex]
2. Rewrite the expression to isolate the square term:
- The simplified form is:
[tex]\[
63.60 - 40c
\][/tex]
- We need to match this with:
[tex]\[
-\square + 20c
\][/tex]
- To do that, we equate:
[tex]\[
63.60 - 40c = -\square + 20c
\][/tex]
3. Isolate and solve for the square term:
- Rearrange the equation:
[tex]\[
63.60 - 40c = -\square + 20c
\][/tex]
- Move the variable term [tex]\(20c\)[/tex] to one side to combine like terms with [tex]\(-40c\)[/tex]:
[tex]\[
63.60 = -\square + 60c
\][/tex]
- Substitute [tex]\(c = 1\)[/tex] to solve for the square term:
[tex]\[
63.60 - 40 \cdot 1 = -(63.60 - 40)
\][/tex]
- This simplifies to:
[tex]\[
\square = 23.6
\][/tex]
Thus, the expression is matched to:
[tex]\[ -23.6 + 20c \][/tex]
So, the detailed solution results in the following:
- The square term is [tex]\(23.6\)[/tex], but since we use it in the form [tex]\(-\square\)[/tex], we get [tex]\(-23.6\)[/tex].
- The coefficient for [tex]\(c\)[/tex] is [tex]\(20\)[/tex].
Final expression:
[tex]\[ -23.6 + 20c \][/tex]
