document.write( "Question 720317: Here is my problem.\r
\n" ); document.write( "\n" ); document.write( "[SQRT(x + 7)] - 2[SQRT(x)] =-2\r
\n" ); document.write( "\n" ); document.write( "OR\r
\n" ); document.write( "\n" ); document.write( "√(x + 7) - 2√(x) = -2 \r
\n" ); document.write( "\n" ); document.write( "-------\r
\n" ); document.write( "\n" ); document.write( "Now, the steps I took to solve this problem are to first square both sides:\r
\n" ); document.write( "\n" ); document.write( "[√(x + 7) - 2√(x)] * [√(x + 7) - 2√(x)] = 4\r
\n" ); document.write( "\n" ); document.write( "so then I FOIL the left side, resulting in:\r
\n" ); document.write( "\n" ); document.write( "(x+7) - [√(x + 7) * - 2√(x)] - [ - 2√(x) * √(x + 7)] + 4x\r
\n" ); document.write( "\n" ); document.write( "So then I thought to subtract (x+7) and (4x) to both sides\r
\n" ); document.write( "\n" ); document.write( " - [√(x + 7) * - 2√(x)] - [ - 2√(x) * √(x + 7)] = 4 - 4x - x - 7 (I think I'm supposed to switch the sign, because I've subtracted it and moved it to the opposite side, right?)\r
\n" ); document.write( "\n" ); document.write( "I think I'm correct up to this point, but now I have to square both sides again.
\n" ); document.write( "I think this left hand side could be re-written as:\r
\n" ); document.write( "\n" ); document.write( " -2[√(x + 7) * - 2√(x)]\r
\n" ); document.write( "\n" ); document.write( "Is this right? I'm subtracting it from itself, a negative, which could simply multiplied by -2. Anyway, now I need to square this again, so I assume the -2 becomes a 4 and I FOIL them separately?
\n" ); document.write( "FOILING the left side will get:\r
\n" ); document.write( "\n" ); document.write( " [√(x + 7) * - 2√(x)] * [√(x + 7) * - 2√(x)]\r
\n" ); document.write( "\n" ); document.write( "Which, when FOILed, looks like\r
\n" ); document.write( "\n" ); document.write( "(x+7) - [√(x+7) * -2√(x)] - [ - 2√(x) * √(x + 7)] + 4x\r
\n" ); document.write( "\n" ); document.write( "It looks exactly the same as before!! I'm just really confused by this problem, and I have a couple more like it, so I want to know if figuring this one out could help me solve the other ones.\r
\n" ); document.write( "\n" ); document.write( "I'm confused about FOILing the different sides, whether or not I can combine two square roots, and quite frankly, a lot of other things.
\n" ); document.write( "One of the options on the test is 9, and I think this is the answer, because I've inserted it into the original equation and it works, but I'm just confused about how to actually get 9 out of this..\r
\n" ); document.write( "\n" ); document.write( "Sorry for the long question. I hope it's not hard to understand. I'm just hoping someone can walk me through all the steps of solving a problem like this so I can do it easily in the future. \n" ); document.write( "

Algebra.Com's Answer #854434 by MathTherapy(10858) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "Here is my problem.\r\n" );
document.write( "\r\n" );
document.write( "[SQRT(x + 7)] - 2[SQRT(x)] =-2   OR   √(x + 7) - 2√(x) = -2 \r\n" );
document.write( "-------\r\n" );
document.write( "Now, the steps I took to solve this problem are to first square both sides:\r\n" );
document.write( "[√(x + 7) - 2√(x)] * [√(x + 7) - 2√(x)] = 4\r\n" );
document.write( "so then I FOIL the left side, resulting in:\r\n" );
document.write( "(x+7) - [√(x + 7) * - 2√(x)] - [ - 2√(x) * √(x + 7)] + 4x\r\n" );
document.write( "So then I thought to subtract (x+7) and (4x) to both sides\r\n" );
document.write( " - [√(x + 7) * - 2√(x)] - [ - 2√(x) * √(x + 7)] = 4 - 4x - x - 7 (I think I'm supposed to switch the sign, because I've\r\n" );
document.write( "subtracted it and moved it to the opposite side, right?)\r\n" );
document.write( "I think I'm correct up to this point, but now I have to square both sides again.\r\n" );
document.write( "I think this left hand side could be re-written as:\r\n" );
document.write( " -2[√(x + 7) * - 2√(x)]\r\n" );
document.write( "Is this right? I'm subtracting it from itself, a negative, which could simply multiplied by -2. Anyway, now I need to\r\n" );
document.write( "square this again, so I assume the -2 becomes a 4 and I FOIL them separately?\r\n" );
document.write( "FOILING the left side will get:\r\n" );
document.write( " [√(x + 7) * - 2√(x)] * [√(x + 7) * - 2√(x)]\r\n" );
document.write( "Which, when FOILed, looks like\r\n" );
document.write( "(x+7) - [√(x+7) * -2√(x)] - [ - 2√(x) * √(x + 7)] + 4x\r\n" );
document.write( "It looks exactly the same as before!! I'm just really confused by this problem, and I have a couple more like it, so I\r\n" );
document.write( "want to know if figuring this one out could help me solve the other ones.\r\n" );
document.write( "\r\n" );
document.write( "I'm confused about FOILing the different sides, whether or not I can combine two square roots, and quite frankly, a lot\r\n" );
document.write( "of other things.\r\n" );
document.write( "One of the options on the test is 9, and I think this is the answer, because I've inserted it into the original\r\n" );
document.write( "equation and it works, but I'm just confused about how to actually get 9 out of this..\r\n" );
document.write( "\r\n" );
document.write( "Sorry for the long question. I hope it's not hard to understand. I'm just hoping someone can walk me through all\r\n" );
document.write( "the steps of solving a problem like this so I can do it easily in the future.\r\n" );
document.write( "*******************************\r\n" );
document.write( "Here is my problem.\r\n" );
document.write( "[SQRT(x + 7)] - 2[SQRT(x)] =-2      OR       √(x + 7) - 2√(x) = -2 \r\n" );
document.write( "-------\r\n" );
document.write( "Now, the steps I took to solve this problem are to first square both sides:\r\n" );
document.write( "[√(x + 7) - 2√(x)] * [√(x + 7) - 2√(x)] = 4\r\n" );
document.write( "so then I FOIL the left side, resulting in:\r\n" );
document.write( "(x+7) - [√(x + 7) * - 2√(x)] - [ - 2√(x) * √(x + 7)] + 4x <=== This is where you went WRONG! When FOILed, this's\r\n" );
document.write( "actually: , which results in:\r\n" );
document.write( "                 . See?          \r\n" );
document.write( "                                                                                                                             \r\n" );
document.write( "                                                      So then I thought to subtract (x+7) and (4x) to both sides\r\n" );
document.write( "                                                      - [√(x + 7) * - 2√(x)] - [ - 2√(x) * √(x + 7)] = 4 - 4x - x - 7\r\n" );
document.write( "                                                                                                     (I think I'm supposed to switch the sign, because I've \r\n" );
document.write( "                                                                                                     subtracted it and moved it to the opposite side, right?)\r\n" );
document.write( "                                                   <=== This is exactly how you need to proceed!\r\n" );
document.write( "                                            ---- Squaring both sides\r\n" );
document.write( "                                                 \r\n" );
document.write( "                                                  \r\n" );
document.write( "                       \r\n" );
document.write( "                                                     OR       \r\n" );
document.write( "                                                                                            \r\n" );
document.write( "                                                                                       9x(x - 9) - 1(x - 9) = 0\r\n" );
document.write( "                                                                                               (x - 9)(9x - 1) = 0\r\n" );
document.write( "                                                                                                x - 9 = 0               OR      9x - 1 = 0\r\n" );
document.write( "                                                                                                      x = 0 + 9        OR           9x = 1\r\n" );
document.write( "                                                                                                      x = 9               OR              x =  (IGNORE)\r\n" );
document.write( " proves to be EXTRANEOUS, so sole solution is: x = 9\r\n" );
document.write( "To some though, it's easier to solve, if one of the left-side RADICALS is MOVED to the right, 1st. But then, this's subjective.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It looks exactly the same as before!! I'm just really confused by this problem, and I have a couple more like it, so I want\r\n" );
document.write( "to know if figuring this one out could help me solve the other ones. Hopefully, the above will clear up SOME/ALL confusion!\r\n" );
document.write( "\r\n" );
document.write( "I'm confused about FOILing the different sides, whether or not I can combine two square roots, and quite frankly, a lot of\r\n" );
document.write( "other things.  Hopefully, the above will clear up SOME/ALL confusion!\r\n" );
document.write( "\r\n" );
document.write( "One of the options on the test is 9, and I think this is the answer, because I've inserted it into the original equation\r\n" );
document.write( "and it works, but I'm just confused about how to actually get 9 out of this.  Yes, the solution is indeed 9, as seen above! \r\n" );
document.write( "\r\n" );
document.write( "Sorry for the long question. I hope it's not hard to understand. I'm just hoping someone can walk me through all the steps\r\n" );
document.write( "of solving a problem like this so I can do it easily in the future.  Hopefully, this author has assisted you in understanding this \r\n" );
document.write( "problem, so you can understand and obtain SOLUTIONS to similar problems, more easily, more efficiently, and without confusion!

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