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The sum of a number and its square is 6. Find the number

2 Answers

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Answer: The sum of a number and its square is 6. Find the number

Explanation:

n + n^2 = 6 n^2 + n - 6 = 0 factoring ___ (n + 3)(n - 2) = 0 n + 3 = 0 ___ n = -3 n - 2 = 0 ___ n = 2 two solutions

User Grena
by
8.9k points
9 votes

Answer:

n = -3, 2

Explanation:

We're given:

  • The sum of a number and its square is 6

Let the number be n.

  • The sum of a number and its square is 6

  • n+n^2=6


n+n^2=6

⇒ Move everything to one side of the equation:


n+n^2-6=0

⇒ Organize in
ax^2+bx+c=0 form:


n^2+n-6=0

⇒ Factor:


n^2-2n+3n-6=0\\n(n-2)+3(n-2)=0\\(n+3)(n-2)=0

⇒ Use the zero-product property to find n:


n+3=0\\n=-3 or
n-2=0\\n=2

User ZhenYu Wang
by
7.8k points

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