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document.write( "Find the real solutions of the equation.\r
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document.write( "x^2 + 3x + sqrt{x^2 + 3x} = 6
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document.write( " x^2 + 3x + 
= 6. (1)\r\n" );
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document.write( "It is a standard equation to solve using \"change of a variable\".\r\n" );
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document.write( "So, we introduce new variable y = .\r\n" );
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document.write( "Then equation (1) takes the form\r\n" );
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document.write( " y^2 + y = 6,\r\n" );
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document.write( "or\r\n" );
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document.write( " y^2 + y - 6 = 0.\r\n" );
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document.write( "We look for non-negative solutions of this equation.\r\n" );
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document.write( "Factor left side\r\n" );
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document.write( " (y+3)*(y-2) = 0\r\n" );
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document.write( "and get two roots y= -3 and y= 2.\r\n" );
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document.write( "For what follows, we consider only positive value y= 2.\r\n" );
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document.write( "The root y= 2 leads to equation \r\n" );
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document.write( " x^2 + 3x = 2^2 = 4,\r\n" );
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document.write( " x^2 + 3x - 4 = 0,\r\n" );
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document.write( " (x+4)*(x-1) = 0 with the solutions x= -4 and x= 1.\r\n" );
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document.write( "Of these two solutions, both work. \r\n" );
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document.write( "ANSWER. There are two real solutions for x: they are x= -4 and x= 1.\r\n" );
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document.write( "Solved.\r
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document.write( "It is a standard way/method of solving similar equations.\r
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document.write( "Similar problem was solved recently at this forum several days ago under this link\r
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document.write( "https://www.algebra.com/algebra/homework/Radicals/Radicals.faq.question.1207632.html\r
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