Hodgson Zimmerman
01/23/2024 · Junior High School
Put the following equation into standard form. \( -5 n^{2}+3 n+2=-6 n^{2}+2+2 n \) \( n^{2}+\square n=0 \)
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Step-by-step Solution
To put the equation \( -5 n^{2}+3 n+2=-6 n^{2}+2+2 n \) into standard form, we first need to simplify and rearrange the equation.
1. Start with the original equation:
\[
-5 n^{2} + 3 n + 2 = -6 n^{2} + 2 + 2 n
\]
2. Move all terms to one side of the equation by adding \( 6 n^{2} \), subtracting \( 2 \), and subtracting \( 2 n \) from both sides:
\[
-5 n^{2} + 6 n^{2} + 3 n - 2 n + 2 - 2 = 0
\]
3. Combine like terms:
\[
(6 n^{2} - 5 n^{2}) + (3 n - 2 n) + (2 - 2) = 0
\]
\[
n^{2} + n + 0 = 0
\]
4. This simplifies to:
\[
n^{2} + n = 0
\]
Now, we can see that the equation is in standard form \( n^{2} + \square n = 0 \), where \( \square = 1 \).
Thus, the final answer is:
\[
n^{2} + 1n = 0
\]
Quick Answer
The equation in standard form is \( n^{2} + 1n = 0 \).
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