Question 122820: If the square of 3 more than a number is 9, find the numbers?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let x be the unknown number.
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Then 3 more than this unknown number is x + 3
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And squaring this quantity is:
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(x + 3)^2
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The problem tells you that this is to equal 9. In equation form this is:
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(x + 3)^2 = 9
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Squaring out the left side results in this equation becoming:
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x^2 + 6 x + 9 = 9
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Subtract 9 from both sides results in:
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x^2 + 6x = 0
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Factor the left side:
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x(x + 6) = 0
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Note that the left side of the equation will be zero if either of the two factors is
equal to zero ... because multiplying by a zero factor will result in an answer of zero.
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So for the two answers, either:
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x = 0
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or
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x + 6 = 0
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In this second case, subtracting 6 from both sides results in:
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x = -6
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So the two answers are x = 0 and x = -6.
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To check these two answers, return to the equation:
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(x + 3)^2 = 9
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Try the first answer we got ... x = 0. Substituting this value of x into the equation
and you get:
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(0 + 3)^2 = 9
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This simplifies to 3^2 = 9 and that, of course, checks out.
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Next in the equation substitute -6 for x and you get:
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(-6 + 3)^2 = 9
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Combining the two numbers in the parentheses leads to:
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(-3)^2 = 9
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And this too is correct because squaring -3 results in +9.
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So our answers of x = 0 and x = -6 are correct.
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Hope this helps you to understand the problem and how to work out an answer.
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