document.write( "Question 921216: Four times the square of a number is 21 more than eight times the number. What is the number? \n" ); document.write( "
Algebra.Com's Answer #558926 by math-vortex(648) $\"\"$ $\"About$
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document.write( "Hi, there---\r\n" );
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document.write( "Your Problem:\r\n" );
document.write( "Four times the square of a number is 21 more than eight times the number.  What is the number?\r\n" );
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document.write( "A Solution:\r\n" );
document.write( "STEP 1. Our first task is to turn these words into algebraic expressions and equations. We are asked to \r\n" );
document.write( "find an unknown number. Let's assign that number a variable. I'll call it n, but you could choose any letter.\r\n" );
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document.write( "\"The square of the number\" is .\r\n" );
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document.write( "\"Four times the square of the number\" is .\r\n" );
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document.write( "\"Eight times the number\" is .\r\n" );
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document.write( "\"21 more than eight times the number is .\r\n" );
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document.write( "STEP 2. Now we make an equation to show that \"four times the square of the number\" and \"21 more than \r\n" );
document.write( "eight times the number\" have the same value. In other words\r\n" );
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document.write( "STEP 3. We have a quadratic equation. We will set it equal to zero. Then we will solve it by factoring, or \r\n" );
document.write( "by using the quadratic formula.\r\n" );
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document.write( "Subtract 8n from both sides of the equation. Then subtract 21 from both sides of the equation. \r\n" );
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document.write( "Now we have a quadratic equation equal to zero. Let's see if we can factor it. The factors of 4 are 4 and \r\n" );
document.write( "1 or 2 and 2. The factors of 21 are 3 and 7 or 21 and 1. We play around with these  to find a sum of -8.\r\n" );
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document.write( "We find that the equation in factored form is \r\n" );
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document.write( "Therefore,  or .\r\n" );
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document.write( "Our solutions are  or .\r\n" );
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document.write( "STEP 4. We need to check out solutions in the original problem. Our first solution is n = -3/2. Substitute \r\n" );
document.write( "-3/2 for \"a number\" in the words of the problem.\r\n" );
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document.write( "Four times the square of -3/2 is (4)(9/4) which equals 9.\r\n" );
document.write( "21 more than 8 times -3/2 is (8)(-3/2) + 21) which is 9.\r\n" );
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document.write( "Now, we check our second solution:  \r\n" );
document.write( "Four times the square of 7/2 is (4)(49/4) which equals 49.\r\n" );
document.write( "21 more than 8 times 7/2 is (8)(7/2) + 21) which is 49.\r\n" );
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document.write( "Therefore, two different numbers make this puzzle true. The number is either -3/2 or 7/2.\r\n" );
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document.write( "Hope this helps. Feel free to email me if you have a question.\r\n" );
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document.write( "Mrs. F\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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