document.write( "Question 75805: If b and 7 are solutions to the equation x^2-4x=a. find the value of a+b. \n" ); document.write( "
Algebra.Com's Answer #54433 by Edwin McCravy(20056)\"\" \"About 
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document.write( "If b and 7 are solutions to the equation\r\n" );
document.write( "x² - 4x = a. find the value of a + b.\r\n" );
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document.write( "x² - 4x = a \r\n" );
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document.write( "is a quadratic equation, and has at most 2 solutions.\r\n" );
document.write( "It is equivalent to\r\n" );
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document.write( "x² - 4x - a = 0 \r\n" );
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document.write( "Since its two solutions are b and 7, then the left side\r\n" );
document.write( "must factor as\r\n" );
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document.write( "(x - b)(x - 7) = 0\r\n" );
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document.write( "x² - 7x - bx + 7b = 0\r\n" );
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document.write( "Factor x out of the two middle terms:\r\n" );
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document.write( "x² + x(-7 - b) + 7b = 0\r\n" );
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document.write( "x² + (-7 - b)x + 7b = 0\r\n" );
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document.write( "Comparing that to\r\n" );
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document.write( "x² - 4x - a = 0\r\n" );
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document.write( "We equate the coefficients of x\r\n" );
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document.write( "-7 - b = -4\r\n" );
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document.write( "Solving that:\r\n" );
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document.write( "   -b = -4+7\r\n" );
document.write( "   -b = 3\r\n" );
document.write( "    b = -3\r\n" );
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document.write( "We also equate the constant terms:\r\n" );
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document.write( "-a = 7b\r\n" );
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document.write( "Substituting -3 for b in that\r\n" );
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document.write( "-a = 7(-3)\r\n" );
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document.write( "-a = -21\r\n" );
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document.write( "a = 21\r\n" );
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document.write( "So a + b = 21 + (-3) = 18\r\n" );
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document.write( "Edwin
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