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SOLVING QUADRATIC EQUATION : Solving by Completing the Square

Introduction
math2ever
Apart from factoring method and quadratic formula, quadratic equation can be solved by using Completing the Square method.

How to solve - Solving Quadratic Equation : Solving by Completing the Square?

To solve a quadratic equation by completing the square.
  1. Divide all terms with value of a.
  2. Isolate the terms in x on one side of the equation.
  3. Add the square of one-half the coefficient of x or ( b 2 ) 2 MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIjxAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGabiGaaiaabeqaamaaeaqbaaGcbaWaaeWaaeaadaWcaaqaaiaadkgaaeaacaaIYaaaaaGaayjkaiaawMcaamaaCaaaleqabaGaaGOmaaaaaaa@3CD0@ to both sides of the equation.
  4. Write the square root of both sides of the resulting equation and solve for x.
Example : Solve the following by using completing the square method.

a) x 2 4x=3{ make sure a is positive 1 x 2 4x+ ( 4 2 ) 2 =3+ ( 4 2 ) 2 { add ( b 2 ) 2 = ( 4 2 ) 2 = ( 2 ) 2 on left of equation = 4 on right of equation x 2 4x+ ( 2 ) 2 =3+4 ( x2 ) 2 =1 ( x2 ) 2 =± 1 x2 =±1 x2=1,x2=1 x=3,x=1 ¯ ¯ MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIjxAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=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1gacaWFHbGaa83Aaiaa=vgacaWFGaGaa83Caiaa=vhacaWFYbGaa8xzaiaa=bcacaWFHbGaa8hiaiaa=LgacaWFZbGaa8hiaiaa=bhacaWFVbGaa83Caiaa=LgacaWF0bGaa8xAaiaa=zhacaWFLbGaa8hiaiaa=fdak8aacaaMc8oacaGL7baaaeaacaWG4bWaaWbaaSqabeaacaaIYaaaaOGaeyOeI0IaaGinaiaadIhacqGHRaWkdaqadaqaaiabgkHiTmaalaaabaGaaGinaaqaaiaaikdaaaaacaGLOaGaayzkaaWaaWbaaSqabeaacaaIYaaaaOGaeyypa0JaeyOeI0IaaG4maiabgUcaRmaabmaabaGaeyOeI0YaaSaaaeaacaaI0aaabaGaaGOmaaaaaiaawIcacaGLPaaadaahaaWcbeqaaiaaikdaaaGccaaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7jugWamaaceaakeaajugWa8qacaWFHbGaa8hzaiaa=rgacaWFGaWaaeWaaSqaaKqzadWaaSaaaSqaaKqzadGaa8NyaaWcbaqcLbmacaaIYaaaaaWccaGLOaGaayzkaaqcLbmadaahaaadbeqaaKqzadGaaGOmaaaacaWF9aWaaeWaaSqaaKqzadWaaSaaaSqaaKqzadGaeyOeI0IaaGinaaWcbaqcLbmacaaIYaaaaaWccaGLOaGaayzkaaqcLbmadaahaaadbeqaaKqzadGaaGOmaaaacqGH9aqpaOWdaiaawUhaaKqzadWdbmaayaaakeaajugWamaabmaaleaajugWaiabgkHiTiaaikdaaSGaayjkaiaawMcaaKqzadWaaWbaaWqabeaajugWaiaaikdaaaaaleaajugWaiaa=9gacaWFUbGaa8hiaiaa=XgacaWFLbGaa8Nzaiaa=rhacaWFGaGaa83Baiaa=zgacaWFGaGaa8xzaiaa=fhacaWF1bGaa8xyaiaa=rhacaWFPbGaa83Baiaa=5gaaOGaayjo+dqcLbmacqGH9aqpdaagaaWcbaqcLbmacaaI0aaameaajugWaiaa=9gacaWFUbGaa8hiaiaa=jhacaWFPbGaa83zaiaa=HgacaWF0bGaa8hiaiaa=9gacaWFMbGaa8hiaiaa=vgacaWFXbGaa8xDaiaa=fgacaWF0bGaa8xAaiaa=9gacaWFUbaaliaawIJ=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@F07E@

b) x 2 +4x+8=0{ make sure a is positive 1 x 2 1 + 4x 1 + 8 1 = 0 1 { divide all terms with -1 x 2 4x8 =0 x 2 4x =8 x 2 4x+ ( 4 2 ) 2 =8+ ( 4 2 ) 2 { add ( b 2 ) 2 = ( 4 2 ) 2 = ( 2 ) 2 on left of equation = 4 on right of equation x 2 4x+ ( 2 ) 2 =8+4 ( x2 ) 2 =12 ( x2 ) 2 =± 12 x2 =±3.46 x2=3.46,x2=3.46 x=5.46,x=1.46 ¯ ¯ MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIjxAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGabiGaaiaabeqaamaaeaqbaaGceiqabiaaiLaa4OqaaiaadkgacaGGPaGaeyOeI0IaamiEamaaCaaaleqabaGaaGOmaaaakiabgUcaRiaaisdacaWG4bGaey4kaSIaaGioaiabg2da9iaaicdacaaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVpaaceaabaqefqvyO9wBHbacgaqcLbmaqqaaaaaaOpGqSvxza8qacaWFTbGaa8xyaiaa=TgacaWFLbGaa8hiaiaa=nhacaWF1bGaa8NCaiaa=vgacaWFGaGaa8xyaiaa=bcacaWFPbGaa83Caiaa=bcacaWFWbGaa83Baiaa=nhacaWFPbGaa8hDaiaa=LgacaWF2bGaa8xzaiaa=bcacaWFXaGcpaGaaGPaVdGaay5EaaaabaWaaSaaaeaacqGHsislcaWG4bWaaWbaaSqabeaacaaIYaaaaaGcbaGaeyOeI0IaaGymaaaacqGHRaWkdaWcaaqaaiaaisdacaWG4baabaGaeyOeI0IaaGymaaaacqGHRaWkdaWcaaqaaiaaiIdaaeaacqGHsislcaaIXaaaaiabg2da9maalaaabaGaaGimaaqaaiabgkHiTiaaigdaaaGaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVpaaceaabaqcLbmapeGaa8hzaiaa=LgacaWF2bGaa8xAaiaa=rgacaWFLbGaa8hiaiaa=fgacaWFSbGaa8hBaiaa=bcacaWF0bGaa8xzaiaa=jhacaWFTbGaa83Caiaa=bcacaWF3bGaa8xAaiaa=rhacaWFObGaa8hiaiaa=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fgacaWFKbGaa8hzaiaa=bcalmaabmaabaWaaSaaaeaajugWaiaa=jgaaSqaaKqzadGaaGOmaaaaaSGaayjkaiaawMcaamaaCaaameqabaqcLbmacaaIYaaaaiaa=1dalmaabmaabaWaaSaaaeaajugWaiabgkHiTiaaisdaaSqaaKqzadGaaGOmaaaaaSGaayjkaiaawMcaamaaCaaameqabaqcLbmacaaIYaaaaiabg2da9aGcpaGaay5EaaWcpeWaaGbaaOqaaSWaaeWaaeaajugWaiabgkHiTiaaikdaaSGaayjkaiaawMcaamaaCaaameqabaqcLbmacaaIYaaaaaWcbaqcLbmacaWFVbGaa8NBaiaa=bcacaWFSbGaa8xzaiaa=zgacaWF0bGaa8hiaiaa=9gacaWFMbGaa8hiaiaa=vgacaWFXbGaa8xDaiaa=fgacaWF0bGaa8xAaiaa=9gacaWFUbaakiaawIJ=aKqzadGaeyypa0ZcdaagaaqaaKqzadGaaGinaaadbaqcLbmacaWFVbGaa8NBaiaa=bcacaWFYbGaa8xAaiaa=DgacaWFObGaa8hDaiaa=bcacaWFVbGaa8Nzaiaa=bcacaWFLbGaa8xCaiaa=vhacaWFHbGaa8hDaiaa=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@7050@

c)2 x 2 x1=0 2 x 2 2 x 2 1 2 = 0 2 x 2 1 2 x 1 2 =0 x 2 1 2 x= 1 2 x 2 1 2 x+ ( 1 2 2 ) 2 = 1 2 + ( 1 2 2 ) 2 x 2 4x+ ( 1 4 ) 2 = 8 16 +( 1 16 ) ( x 1 4 ) 2 = 9 16 x 1 4 =± 9 16 x2 =±3.46 x2=3.46,x2=3.46 x=5.46,x=1.46 ¯ ¯ MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIjxAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=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@4ADF@


d)2 x 2 x3=0 2 x 2 x3 2 = 0 2 x 2 x 2 3 2 =0 x 2 1 2 x 3 2 =0 x 2 1 2 x+ ( 1 2 2 ) 2 = 3 2 + ( 1 2 2 ) 2 x 2 1 2 x+ ( 1 4 ) 2 = 3 2 + ( 1 4 ) 2 ( x 1 4 ) 2 = 3 2 + 1 16 ( x 1 4 ) 2 = 25 16 ( x 1 4 ) 2 = 25 16 ( x 1 4 ) 2 =± 25 16 x 1 4 =± 5 4 x= 1 4 ± 5 4 x= 6 4 orx= 4 4 x= 3 2 orx=1 MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgiofMCY92DaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVeYhLipgYlb91rFfpec8Eeeu0xXdbba9frFj0=OqFfea0dXdc9xs=e0hfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=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jhakiaaykW7caaMc8UaaGPaVlaaykW7caWG4bGaaGPaVlaaykW7cqGH9aqpcaaMc8UaaGPaVlabgkHiTmaaleaaleaacaaI0aaabaGaaGinaaaaaOqaaiaadIhacaaMc8UaaGPaVlabg2da9iaaykW7caaMc8+aaSqaaSqaaiaaiodaaeaacaaIYaaaaOGaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7jaaycaWFVbGaa8NCaOGaaGPaVlaaykW7caaMc8UaaGPaVlaadIhacaaMc8UaaGPaVlabg2da9iaaykW7caaMc8UaeyOeI0IaaGymaaaaaa@BF40@
Try it yourself - Solving Quadratic Equation : Solving quadratic equation by using Completing the Square

a)4 x 2 8x5=0 b)2 x 2 x6=0 c)12 x 2 18x=0 } ans-x= 5 2 , 1 2 ans-x=2, 3 2 ans-x=0, 3 2 MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIjxAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGabiGaaiaabeqaamaaeaqbaaGcbaWaaiGaaqaabeqaaiaadggacaGGPaaeaaaaaaaaa8qacaaI0aGaamiEa8aadaahaaWcbeqaa8qacaaIYaaaaOGaeyOeI0IaaGioaiaadIhacqGHsislcaaI1aGaeyypa0JaaGimaaWdaeaacaWGIbGaaiyka8qacaaIYaGaamiEa8aadaahaaWcbeqaa8qacaaIYaaaaOGaeyOeI0IaamiEaiabgkHiTiaaiAdacqGH9aqpcaaIWaaapaqaaiaadogacaGGPaGaaGPaV=qacaaIXaGaaGOmaiaadIhapaWaaWbaaSqabeaapeGaaGOmaaaakiabgkHiTiaaigdacaaI4aGaamiEaiabg2da98aacaaIWaaaaiaaw2haauaabeqadeaaaeaaruavHH2BTfgaiyaajugWaabbaaaaaG+acXwDLbWdciaa=fgacaWFUbGaa83Caiaa=1capaGaamiEaiabg2da9SWaaSaaaeaacaaI1aaabaGaaGOmaaaajugWaiaacYcacqGHsisllmaalaaabaGaaGymaaqaaiaaikdaaaaakeaajugWa8GacaWFHbGaa8NBaiaa=nhacaWFTaWdaiaadIhacqGH9aqpcaaIYaGaaiilaiabgkHiTSWaaSaaaeaacaaIZaaabaGaaGOmaaaaaOqaaKqzadWdciaa=fgacaWFUbGaa83Caiaa=1capaGaamiEaiabg2da9iaaicdacaGGSaWcdaWcaaqaaiaaiodaaeaacaaIYaaaaaaaaaa@808A@

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