document.write( "Question 51882: x^2-15=2x \n" ); document.write( "
Algebra.Com's Answer #34598 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
x² - 15 = 2x\r\n" );
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document.write( "Get 0 on the right by adding -2x to both sides.\r\n" );
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document.write( "x² - 15 - 2x = 0\r\n" );
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document.write( "Arrange the left side in descending order of\r\n" );
document.write( "eponents of x:\r\n" );
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document.write( "We need to factor the left side:\r\n" );
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document.write( "Give the x² the coefficient of 1\r\n" );
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document.write( "1x² - 2x - 15 = 0\r\n" );
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document.write( "Multiply the red 1 by the blue 15, getting 15.\r\n" );
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document.write( "Now think of a pair of positive integers whose product\r\n" );
document.write( "is the blue 15 and whose difference is the green 2.\r\n" );
document.write( "I said difference because the last sign (before the\r\n" );
document.write( "15) is minus. Had it been plus, I would have said \"sum\".\r\n" );
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document.write( "We think of the integers 3 and 5 because their product is \r\n" );
document.write( "the blue 15 and their difference is the green 2.\r\n" );
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document.write( "Now we use the 3 and 5 to rewrite the green -2 as 3 - 5.\r\n" );
document.write( "So we rewrite 2x as -3x + 5x. That is, \r\n" );
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document.write( "     x² - 2x - 15 = 0\r\n" );
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document.write( "becomes\r\n" );
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document.write( "x² + 3x - 5x - 15 = 0\r\n" );
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document.write( "Now we factor x out of the first two terms\r\n" );
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document.write( "x(x + 3) - 5x - 15 = 0\r\n" );
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document.write( "and factor -5 out of the last two terms on the\r\n" );
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document.write( "x(x + 3) - 5(x + 3) = 0\r\n" );
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document.write( "Be careful to notice that when we factor a\r\n" );
document.write( "NEGATIVE number, -5, out of another NEGATIVE\r\n" );
document.write( "number -15, we get a POSITIVE 3.\r\n" );
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document.write( "Now we have a common factor, which we can\r\n" );
document.write( "factor out, namely the (x + 3)'s which I \r\n" );
document.write( "color red:\r\n" );
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document.write( "x(x + 3) - 5(x + 3) = 0 \r\n" );
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document.write( "Factor out the red parentheses:\r\n" );
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document.write( "(x + 3)(x - 5) = 0\r\n" );
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document.write( "Setting the first factor (x + 3) = 0 gives x = -3\r\n" );
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document.write( "Setting the second factor (x - 5) = 0 gives x = 5\r\n" );
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document.write( "So the solutions are -3 and 5.\r\n" );
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document.write( "Edwin
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