![\"\"](\"/images/stars/stars-13.gif\")
You can put this solution on YOUR website!
.
\n" ); document.write( "
\r\n" );
document.write( "|x^2 - 4x - 4 | = 8 (1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The equation (1) is equivalent to this:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " Find the solution set to this set of equations:\r\n" );
document.write( "\r\n" );
document.write( " EITHER x^2 - 4x - 4 = 8 (2)\r\n" );
document.write( " OR x^2 - 4x - 4 = -8. (3)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Notice that these two equations, (2) and (3), are connected by the logical term \"OR\",\r\n" );
document.write( "\r\n" );
document.write( "which means that the set of solutions to equation (1) is the UNION of solutions to equations (2) and (3).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now,\r\n" );
document.write( "\r\n" );
document.write( " x^2 - 4x - 4 = 8 ====> x^2 - 4x - 12 = 0 ====> (x+2)\*(c-6) = 0 ====> the solutions are x = -2 and/or x = 6,\r\n" );
document.write( "\r\n" );
document.write( "and\r\n" );
document.write( "\r\n" );
document.write( " x^2 - 4x - 4 = -8 ====> x^2 - 4x + 4 = 0 ====> (x-2)^2 = 0 ====> the solution is x = 2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus the solution to the given equation (1) is the set {-2, 2, 6}.\r\n" );
document.write( "\r\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Plot y = |x^2 - 4x - 4| (red) and y = 8 (green)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "--------------
\n" ); document.write( "On solving Absolute Value equations there is a bunch of lessons in this site \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( " - OVERVIEW of lessons on Absolute Value equations \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Read them attentively and become an expert in this area.\r
\n" ); document.write( "
\n" ); document.write( "
\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
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic
\n" ); document.write( "\"Solving Absolute values equations\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
\n" ); document.write( "
\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
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "