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|00000000| 54 55 54 4f 52 20 30 36 | 8c 0e 00 00 6a 00 00 00 |TUTOR 06|....j...|
|00000010| 53 65 63 74 69 6f 6e 20 | 31 2e 36 20 20 4f 74 68 |Section |1.6  Oth|
|00000020| 65 72 20 54 79 70 65 73 | 20 6f 66 20 45 71 75 61 |er Types| of Equa|
|00000030| 74 69 6f 6e 73 0d 0b 00 | 46 6f 72 20 6d 6f 72 65 |tions...|For more|
|00000040| 20 70 72 61 63 74 69 63 | 65 3a 0d 0a 00 0d 0a 00 | practic|e:......|
|00000050| 20 20 20 20 20 10 31 2d | 36 2d 33 0e 78 31 2d 36 |     .1-|6-3.x1-6|
|00000060| 0e 45 78 65 72 63 69 73 | 65 73 0f 0d 0a 00 20 20 |.Exercis|es....  |
|00000070| 20 20 20 10 31 2d 36 2d | 32 0e 65 31 2d 36 0e 47 |   .1-6-|2.e1-6.G|
|00000080| 75 69 64 65 64 20 45 78 | 65 72 63 69 73 65 73 0f |uided Ex|ercises.|
|00000090| 0d 0a 00 0d 0a 00 54 6f | 70 69 63 73 20 66 6f 72 |......To|pics for|
|000000a0| 20 65 78 70 6c 6f 72 61 | 74 69 6f 6e 3a 0d 0a 00 | explora|tion:...|
|000000b0| 0d 0a 00 20 20 20 20 20 | 0e 73 31 2d 36 2d 31 0e |...     |.s1-6-1.|
|000000c0| 53 6f 6c 76 69 6e 67 20 | 50 6f 6c 79 6e 6f 6d 69 |Solving |Polynomi|
|000000d0| 61 6c 20 45 71 75 61 74 | 69 6f 6e 73 0f 0d 0a 00 |al Equat|ions....|
|000000e0| 20 20 20 20 20 0e 73 31 | 2d 36 2d 32 0e 53 6f 6c |     .s1|-6-2.Sol|
|000000f0| 76 69 6e 67 20 45 71 75 | 61 74 69 6f 6e 73 20 49 |ving Equ|ations I|
|00000100| 6e 76 6f 6c 76 69 6e 67 | 20 52 61 64 69 63 61 6c |nvolving| Radical|
|00000110| 73 0f 0d 0a 00 20 20 20 | 20 20 0e 73 31 2d 36 2d |s....   |  .s1-6-|
|00000120| 33 0e 53 6f 6c 76 69 6e | 67 20 45 71 75 61 74 69 |3.Solvin|g Equati|
|00000130| 6f 6e 73 20 49 6e 76 6f | 6c 76 69 6e 67 20 46 72 |ons Invo|lving Fr|
|00000140| 61 63 74 69 6f 6e 73 20 | 6f 72 20 41 62 73 6f 6c |actions |or Absol|
|00000150| 75 74 65 20 56 61 6c 75 | 65 0f 0d 0a 00 53 65 63 |ute Valu|e....Sec|
|00000160| 74 69 6f 6e 20 31 2e 36 | 20 20 4f 74 68 65 72 20 |tion 1.6|  Other |
|00000170| 54 79 70 65 73 20 6f 66 | 20 45 71 75 61 74 69 6f |Types of| Equatio|
|00000180| 6e 73 0d 0b 00 41 74 20 | 74 68 69 73 20 70 6f 69 |ns...At |this poi|
|00000190| 6e 74 2c 20 77 65 20 68 | 61 76 65 20 6f 6e 6c 79 |nt, we h|ave only|
|000001a0| 20 66 6f 75 72 20 62 61 | 73 69 63 20 6d 65 74 68 | four ba|sic meth|
|000001b0| 6f 64 73 20 66 6f 72 20 | 73 6f 6c 76 69 6e 67 20 |ods for |solving |
|000001c0| 6e 6f 6e 6c 69 6e 65 61 | 72 20 0d 0a 00 65 71 75 |nonlinea|r ...equ|
|000001d0| 61 74 69 6f 6e 73 3a 20 | 66 61 63 74 6f 72 69 6e |ations: |factorin|
|000001e0| 67 2c 20 63 6f 6d 70 6c | 65 74 69 6e 67 20 74 68 |g, compl|eting th|
|000001f0| 65 20 73 71 75 61 72 65 | 2c 20 65 78 74 72 61 63 |e square|, extrac|
|00000200| 74 69 6e 67 20 72 6f 6f | 74 73 20 61 6e 64 20 74 |ting roo|ts and t|
|00000210| 68 65 20 0d 0a 00 51 75 | 61 64 72 61 74 69 63 20 |he ...Qu|adratic |
|00000220| 46 6f 72 6d 75 6c 61 2e | 20 20 54 68 65 72 65 66 |Formula.|  Theref|
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|00000240| 72 6e 20 74 6f 20 72 65 | 77 72 69 74 65 20 6e 6f |rn to re|write no|
|00000250| 6e 6c 69 6e 65 61 72 20 | 65 71 75 61 74 69 6f 6e |nlinear |equation|
|00000260| 73 20 0d 0a 00 69 6e 20 | 61 20 66 6f 72 6d 20 74 |s ...in |a form t|
|00000270| 6f 20 77 68 69 63 68 20 | 77 65 20 63 61 6e 20 61 |o which |we can a|
|00000280| 70 70 6c 79 20 6f 6e 65 | 20 6f 66 20 74 68 65 73 |pply one| of thes|
|00000290| 65 20 6d 65 74 68 6f 64 | 73 2e 20 20 0d 0a 00 0d |e method|s.  ....|
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|00000360| 20 20 11 33 61 75 20 20 | 2b 20 62 75 20 2b 20 63 |  .3au  |+ bu + c|
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|00000390| 64 20 11 33 75 20 11 31 | 69 73 20 61 6e 20 61 6c |d .3u .1|is an al|
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|000004a0| 20 20 11 33 33 28 78 20 | 2d 20 32 29 20 2d 20 32 |  .33(x |- 2) - 2|
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|00000540| 6f 6e 20 31 2e 36 20 20 | 4f 74 68 65 72 20 54 79 |on 1.6  |Other Ty|
|00000550| 70 65 73 20 6f 66 20 45 | 71 75 61 74 69 6f 6e 73 |pes of E|quations|
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|00000680| 72 65 20 62 6f 74 68 20 | 73 69 64 65 73 2e 20 20 |re both |sides.  |
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|000008b0| 20 20 20 21 11 33 78 20 | 20 20 11 34 21 20 20 20 |   !.3x |  .4!   |
|000008c0| 20 11 31 3d 20 38 0d 0b | 00 20 20 20 20 20 20 20 | .1= 8..|.       |
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|00000d50| 63 61 6e 20 62 65 20 70 | 6f 73 69 74 69 76 65 20 |can be p|ositive |
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|00000d70| 00 54 68 69 73 20 72 65 | 73 75 6c 74 73 20 69 6e |.This re|sults in|
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|00000e10| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 33 78 |        |     .3x|
|00000e20| 20 11 31 2b 20 31 20 3d | 20 35 20 20 20 20 20 61 | .1+ 1 =| 5     a|
|00000e30| 6e 64 20 20 20 20 20 2d | 28 11 33 78 20 11 31 2b |nd     -|(.3x .1+|
|00000e40| 20 31 29 20 3d 20 35 0d | 0a 00 0d 0b 00 77 68 69 | 1) = 5.|.....whi|
|00000e50| 63 68 20 69 6d 70 6c 69 | 65 73 20 74 68 61 74 20 |ch impli|es that |
|00000e60| 74 68 65 20 65 71 75 61 | 74 69 6f 6e 20 68 61 73 |the equa|tion has|
|00000e70| 20 74 77 6f 20 73 6f 6c | 75 74 69 6f 6e 73 3a 20 | two sol|utions: |
|00000e80| 34 20 61 6e 64 20 2d 36 | 2e 0d 0a 00 35 00 00 00 |4 and -6|....5...|
|00000e90| 28 01 00 00 4d 25 00 00 | 10 00 00 00 00 00 00 00 |(...M%..|........|
|00000ea0| 73 31 2d 36 00 82 01 00 | 00 b9 03 00 00 4d 25 00 |s1-6....|.....M%.|
|00000eb0| 00 5d 01 00 00 00 00 00 | 00 73 31 2d 36 2d 31 00 |.]......|.s1-6-1.|
|00000ec0| 60 05 00 00 c8 04 00 00 | 4d 25 00 00 3b 05 00 00 |`.......|M%..;...|
|00000ed0| 00 00 00 00 73 31 2d 36 | 2d 32 00 4d 0a 00 00 3f |....s1-6|-2.M...?|
|00000ee0| 04 00 00 4d 25 00 00 28 | 0a 00 00 00 00 00 00 73 |...M%..(|.......s|
|00000ef0| 31 2d 36 2d 33 00       |                         |1-6-3.  |        |
+--------+-------------------------+-------------------------+--------+--------+