Answered

Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Join our Q&A platform and connect with professionals ready to provide precise answers to your questions in various areas. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

Solve the equation:

[tex]\[ \square + 14x - \square - 13x + 3x^2 = 23x^2 + x \][/tex]

Sagot :

GinnyAnswer
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.
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.