document.write( "Question 115555: I really need help with this problem. The problem says to find two consecutive intergers whose product is 90, it must be solved algebraically. Thank You. \n" ); document.write( "
Algebra.Com's Answer #84114 by bucky(2189)\"\" \"About 
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Two unknown consecutive integers can be represented by x and x+1 since the second integer must
\n" ); document.write( "be one greater than the first one ... because they are consecutive.
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\n" ); document.write( "The product of these two integers is then given by:
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\n" ); document.write( "x*(x + 1)
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\n" ); document.write( "and this product must equal 90. This makes the equation become:
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\n" ); document.write( "x*(x+1) = 90
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\n" ); document.write( "And multiplying out the left side results in the equation:
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\n" ); document.write( "x^2 + x = 90
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\n" ); document.write( "Get rid of the 90 on the left side by subtracting 90 from both sides to get:
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\n" ); document.write( "x^2 + x - 90 = 0
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\n" ); document.write( "You can solve this by graphing it and seeing at what values of x the graph crosses the
\n" ); document.write( "x-axis. Or you can use the quadratic formula which is a short way of completing the square,
\n" ); document.write( "or you can factor it.
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\n" ); document.write( "Let's use the quadratic formula which says that for a quadratic equation of the standard form:
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\n" ); document.write( "ax^2 + bx + c = 0
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\n" ); document.write( "the values of x that satisfy this equation are given by:
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\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
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\n" ); document.write( "Compare our equation to the standard quadratic form. When you do you will see that \"a\" which
\n" ); document.write( "is the multiplier of x must be 1. b which is the multiplier of x must also be 1. And c which is
\n" ); document.write( "the constant must be -90. Substitute these values into the equation for x and you get:
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\n" ); document.write( "\"x+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A-90+%29%29%2F%282%2A1%29+\"
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\n" ); document.write( "The term inside the radical sign multiplies out to become \"1+%2B+360+=+361\". This changes the
\n" ); document.write( "answer to:
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\n" ); document.write( "\"x+=+%28-1+%2B-+sqrt%28+361+%29%29%2F%282%2A1%29+\"
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\n" ); document.write( "but the square root of 361 is 19. So you can replace the radical by 19 and the answers for x
\n" ); document.write( "are then:
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-1+%2B-+19%29%2F%282%2A1%29+\"
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\n" ); document.write( "Notice that the denominator multiplies out to 2 which makes the problem:
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\n" ); document.write( "\"x+=+%28-1+%2B-+19%29%2F2+\"
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\n" ); document.write( "The two possible answers are then:
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\n" ); document.write( "\"x+=+%28-1-19%29%2F2+=+-20%2F2+=+-10\" and
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\n" ); document.write( "\"x+=+%28-1+%2B+19%29%2F2+=+18%2F2+=+9\"
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\n" ); document.write( "If x is -10, then the next consecutive integer is -10 + 1 = -9. This means the consecutive
\n" ); document.write( "integers -10 and -9 are one answer.
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\n" ); document.write( "If x is +9, then the next consecutive integer is +9 + 1 = +10. This means the consecutive
\n" ); document.write( "integers +9 and +10 are another answer.
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\n" ); document.write( "Check: -10 times -9 = +90. That checks. And +9 times +10 = +90. That also checks. So
\n" ); document.write( "our two answers are correct.
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\n" ); document.write( "Hope this helps you with this problem.
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