SOLUTION: when the sum of a number plus 2 is squared, it is 16 more than the square of that number. what is the number?

Question 621094: when the sum of a number plus 2 is squared, it is 16 more than the square of that number. what is the number?

Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!
Hi, there--
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This is basically a problem about translating from English to algebraic expressions. We'll just translate piece by piece.
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Let n be the number we are interested in.
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In algebra, the phrase "the sum of the number plus 2 is squared" is written as .
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The phrase, "16 more than the square of the number" is written as .
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These two expressions are equal to each other, so we have the equation,

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We solve for n to find the number.

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Simplify by combining like terms. Subtract n^2 from both sides of the equation.

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Subtract 4 from both sides of the equation.

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In the context of this problem, n=3 means that the number is 3.
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We need to check our answer using the information in the original problem.
"The sum of 3 plus 2 is squared" gives us 5-squared, or 25.
"16 more than 3-squared gives us 16 plus 9, or 25.
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Our answer is correct because both sides of the equation are equal. The number is 3.
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Hope this helps! Feel free to email me if you have questions about this solution.
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Ms.Figgy
math.in.the.vortex@gmail.com

when the sum of a number plus 2 is squared, it is 16 more than the square of that number. what is the number?
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