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What is complete the square method |
| Answer» The given equation is:7x2\xa0+ 3x - 4 = 0Multiply each term by 7, we obtain:\xa049x2\xa0+ 21x - 28 = 0{tex}\\Rightarrow{/tex}\xa049x2\xa0+ 21x = -28On adding\xa0{tex}\\left( \\frac { 3 } { 2 } \\right) ^ { 2 }{/tex} on both sides, we get(7x)2\xa0+ 2\xa0{tex}\\times{/tex}\xa07x\xa0{tex}\\times \\frac { 3 } { 2 } + \\left( \\frac { 3 } { 2 } \\right) ^ { 2 } = 28 + \\left( \\frac { 3 } { 2 } \\right) ^ { 2 }{/tex}\xa0{tex}\\Rightarrow \\left( 7 x + \\frac { 3 } { 2 } \\right) ^ { 2 } = 28 + \\frac { 9 } { 4 }{/tex}{tex}\\Rightarrow \\left( 7 x + \\frac { 3 } { 2 } \\right) ^ { 2 } = \\frac { 121 } { 4 }{/tex}{tex}\\Rightarrow 7 x + \\frac { 3 } { 2 } = \\pm \\frac { 11 } { 2 }{/tex}Therefore, either 7x =\xa0{tex}- \\frac { 3 } { 2 } - \\frac { 11 } { 2 }{/tex}\xa0or 7x =\xa0{tex}- \\frac { 3 } { 2 } + \\frac { 11 } { 2 }{/tex}{tex}\\Rightarrow{/tex}\xa07x = -7 or 7x = 4{tex}\\Rightarrow{/tex}\xa0x = -1 or x =\xa0{tex}\\frac { 4 } { 7 }{/tex}Hence, the roots of given equation are {tex}\\frac { 4 } { 7 }{/tex} and\xa0-1. | |