document.write( "Question 498825: I don't understand how to solve this problem. Thank you.\r
\n" ); document.write( "\n" ); document.write( "It says solve and check the quadratic equation below by taking the square root of both sides. Express irrational answers in rational form.\r
\n" ); document.write( "\n" ); document.write( "(x-10)^2=4\r
\n" ); document.write( "\n" ); document.write( "thank you so much \n" ); document.write( "

Algebra.Com's Answer #852313 by ikleyn(52835) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Solve and check the quadratic equation below by taking the square root of both sides. Express irrational answers in rational form.
\n" ); document.write( "(x-10)^2=4
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\n" ); document.write( "\n" ); document.write( "        In his post, tutor @Theo lost some solutions to given equations.\r
\n" ); document.write( "\n" ); document.write( "        So, his treatment of the problem is incomplete.\r
\n" ); document.write( "\n" ); document.write( "        I came to bring a correct complete solutions.\r
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document.write( "Your starting equation is\r\n" );
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document.write( "    (x-10)^2 = 4.    (1)\r\n" );
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document.write( "Take square root of both sides.  You will get\r\n" );
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document.write( "    x-10 = +/-2.         <<<---===  square root of 4 has two values: 2 and -2.\r\n" );
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document.write( "It means that we have two cases.\r\n" );
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document.write( "Case 1.  x-10 = 2.   Then  x = 2+10 = 12.\r\n" );
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document.write( "Case 2.  x-10 = -2.  Then  x = -2+10 = 8.\r\n" );
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document.write( "So, equation (1) has two solutions.  They are  x = 8  and  x = 12.\r\n" );
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document.write( "Check.  Substitute these values into equation (1) to make sure that they suit perfectly.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved correctly.\r
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\n" ); document.write( "\n" ); document.write( "It might seem the loss of roots is a minor issue.\r
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\n" ); document.write( "\n" ); document.write( " In fact, it is not so.\r
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\n" ); document.write( "\n" ); document.write( "Loss of roots is a failed test of understanding square roots.
\n" ); document.write( "So, solving this equation correctly or incorrectly is an easy way
\n" ); document.write( "to check if a person does understand the subject.
\n" ); document.write( "In 10 seconds, everything becomes clear.\r
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\n" ); document.write( "\n" ); document.write( "Notice that the problem's formulation is like a lame horse with three legs.\r
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\n" ); document.write( "\n" ); document.write( "Indeed, it says \" Express irrational answers in rational form. \"\r
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\n" ); document.write( "\n" ); document.write( "Firstly, it is IMPOSSIBLE to do.\r
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\n" ); document.write( "\n" ); document.write( "Secondly, it shows that a person, who wrote it, is mathematically illiterate.\r
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