document.write( "Question 1092338: Find all solutions of the equation |x^2 - 14x + 29| = 4. Discuss whether or not your solution generates extraneous solutions. \n" ); document.write( "

Algebra.Com's Answer #706950 by ikleyn(52908) $\"\"$ $\"About$

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\n" ); document.write( "Find all solutions of the equation |x^2 - 14x + 29| = 4. Discuss whether or not your solution generates extraneous solutions.
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document.write( "You need to solve actually two quadratic equations\r\n" );
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document.write( "1)  x^2 - 14x + 29 = 4,      (1)     and\r\n" );
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document.write( "2)  x^2 - 14x + 29 = -4      (2)\r\n" );
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document.write( "independently, and then to take the union of their roots as a set of solutions to the absolute value equation.\r\n" );
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document.write( "So, start from eq(1).\r\n" );
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document.write( "x^2 - 14x + 29 = 4  ====>  x^2 - 14x + (29-4) = 0  ====>\r\n" );
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document.write( "x^2 - 14x + 25 = 0  ====>   =  =  =  = .\r\n" );
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document.write( "Now work on eqn(2)\r\n" );
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document.write( "x^2 - 14x + 29 = -4  ====>  x^2 - 14x + (29 +4) = 0  ====>  \r\n" );
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document.write( "x^2 - 14x + 33 = 0  ====>   =  =  = .\r\n" );
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document.write( "So, the solutions to your original equation are these four real numbers:\r\n" );
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document.write( ",  ,    and  .\r\n" );
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\n" ); document.write( "\n" ); document.write( "Plot y = $\"abs%28x%5E2+-+14x+%2B+29%29\"$ and y = 4.\r
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\n" ); document.write( "\n" ); document.write( "These four solutions are x-coordinates of intersection points.\r
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\n" ); document.write( "\n" ); document.write( "My solution did not produce extraneous solutions.\r
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\n" ); document.write( "\n" ); document.write( "---------------
\n" ); document.write( "On solving absolute value equations see the lessons \r
\n" ); document.write( "\n" ); document.write( "    - Absolute Value equations\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 1\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 2\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 3\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO solve equations containing Quadratic Terms under the Absolute Value sign. Lesson 1\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO solve equations containing Quadratic Terms under the Absolute Value sign. Lesson 2\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I\r
\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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