Algebra.Com's Answer #774489 by ikleyn(52781)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
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document.write( " The solution can be done in much simpler way.\r
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document.write( " +  +  = 17 (1)\r\n" );
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document.write( " + = 17 - \r\n" );
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document.write( "Square both sides\r\n" );
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document.write( "(10-x) +  + (3+x) = 17 -  + 4*(30 +7x - x^2)\r\n" );
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document.write( "Notice that (10-x)*(3+x) = 30 + 7x - x^2, and continue transform preceding equations\r\n" );
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document.write( "(10-x) + + (3+x) = 289 - + 4*(30 +7x - x^2)\r\n" );
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document.write( "13 + = 289 - + 4*(30+7x-x^2)\r\n" );
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document.write( "0 = 276 -  + 4*(30+7x-x^2) (2)\r\n" );
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document.write( "Introduce new variable t =  .\r\n" );
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document.write( "Then equation (2) takes the form\r\n" );
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document.write( "4t^2 - 70t + 276 = 0.\r\n" );
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document.write( "Solve it using the quadratic formula\r\n" );
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document.write( " =  =  =  .\r\n" );
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document.write( "Case 1. t =  = -6.\r\n" );
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document.write( " Then t = = -6 implies (after squaring both sides)\r\n" );
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document.write( " 30 + 7x - x^2 = 36\r\n" );
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document.write( " x^2 - 7x + 6 = 0\r\n" );
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document.write( " (x-1)*(x-6) = 0\r\n" );
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document.write( " The roots are x= 1 and x= 6.\r\n" );
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document.write( " You can easily check that both these roots satisfy the original equation.\r\n" );
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document.write( "Case 2. t =  = -11.5.\r\n" );
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document.write( " Then t = = -11.5 implies (after squaring both sides)\r\n" );
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document.write( " 30 + 7x - x^2 = 132.25\r\n" );
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document.write( " x^2 - 7x + 102.25 = 0\r\n" );
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document.write( " Discriminant d = b^2 - 4ac = 7^2 - 4*102.25 is negative,\r\n" );
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document.write( " Hence, this case does not produce real solutions.\r\n" );
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document.write( "The solution is completed.\r\n" );
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document.write( "The ANSWER is: the original equation has two solutions x= 1 and x= 6.\r\n" );
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document.write( "Solved.\r
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document.write( "In her solution, tutor @MathLover1 makes a HUGE amount unnecessary work.\r
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document.write( "Also, on the way, she applies (without acknowledgement) Internet software to factor polynomials of high degrees (up to 8-th degree).\r
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document.write( " It is IMPOSSIBLE to get such factoring \"by hands\", without using software tools.\r\n" );
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document.write( "Obviously, this way is not accessible for real school Math student, and it is NOT the WAY to solve such problem for educational purposes.\r
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document.write( "The way which I propose in my post, is a real way, and, actually, the only real, accessible and right way to solve this problem.\r
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