Let's solve the equation step by step. The equation given is:
[tex]\[
\square + 14x - \square - 13x + 3x^2 = 23x^2 + x
\][/tex]
1. Identify and group like terms on the left-hand side:
- The terms involving [tex]\(x^2\)[/tex]: [tex]\(3x^2\)[/tex]
- The terms involving [tex]\(x\)[/tex]: [tex]\(14x - 13x\)[/tex]
- The constants or unspecified terms: [tex]\(\square, -\square\)[/tex]
2. Combine the [tex]\(x\)[/tex] terms on the left-hand side:
- [tex]\(14x - 13x = 1x\)[/tex]
3. Re-write the equation with the known terms combined:
[tex]\[
\square + 1x - \square + 3x^2 = 23x^2 + x
\][/tex]
4. Compare both sides of the equation to match coefficients:
- The coefficient of [tex]\(x^2\)[/tex] on the left-hand side must equal the coefficient of [tex]\(x^2\)[/tex] on the right-hand side.
- The coefficient of [tex]\(x\)[/tex] on the left-hand side must equal the coefficient of [tex]\(x\)[/tex] on the right-hand side.
- The constant terms must balance out (though in this case, there are no constants given explicitly).
5. Match the coefficients for the [tex]\(x^2\)[/tex] terms:
- On the left: [tex]\(3x^2\)[/tex]
- On the right: [tex]\(23x^2\)[/tex]
- But since [tex]\(3\)[/tex] does not match [tex]\(23\)[/tex], and we only add or subtract constants, we do not change the coefficients in [tex]\(x^2\)[/tex].
Because we only have these elements on both sides:
[tex]\[
3x^2 = 23x^2
\][/tex]
This indicates that our initial constants (placeholders, labeled as [tex]\(\square\)[/tex] and [tex]\(-\square\)[/tex]), might be zero to ensure the equation balances in [tex]\(x^2\)[/tex].
6. Check the coefficients for the [tex]\(x\)[/tex] terms:
- On the left: [tex]\(1x\)[/tex]
- On the right: [tex]\(1x\)[/tex]
- Both sides match in that respect.
7. Align the constants, the unspecified placeholders:
- Since there's no standalone constant term given, check by setting unspecified parts to zero:
- [tex]\(( \square + - \square)_|0 + 1x + 3x^2 = 23 x^2 + x \)[/tex]
8. Solution:
- The missing terms (placeholders [tex]\(\square\)[/tex]) must equal [tex]\(0\)[/tex] to balance the equation.
Therefore, the missing terms are:
[tex]\[
(\square, \square) = (0, 0)
\][/tex]
Thus, both missing terms are 0.
