Réitigh x=1/x+1/6

$$x = \frac { 1 } { x } + \frac { 1 } { 6 }$$

Réitigh do x.

$$x = \frac{\sqrt{145} + 1}{12} \approx 1.086799548$$

$$x=\frac{1-\sqrt{145}}{12}\approx -0.920132882$$

Céimeanna ag Baint Úsáid as an bhFoirmle Chearnach

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de x agus 6 ná 6x. Méadaigh \frac{1}{x} faoi \frac{6}{6}. Méadaigh \frac{1}{6} faoi \frac{x}{x}.

$$x=\frac{6}{6x}+\frac{x}{6x}$$

Tá an t-ainmneoir céanna ag \frac{6}{6x} agus \frac{x}{6x} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$x=\frac{6+x}{6x}$$

Bain \frac{6+x}{6x} ón dá thaobh.

$$x-\frac{6+x}{6x}=0$$

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Méadaigh x faoi \frac{6x}{6x}.

$$\frac{x\times 6x}{6x}-\frac{6+x}{6x}=0$$

Tá an t-ainmneoir céanna ag \frac{x\times 6x}{6x} agus \frac{6+x}{6x} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$\frac{x\times 6x-\left(6+x\right)}{6x}=0$$

Déan iolrúcháin in x\times 6x-\left(6+x\right).

$$\frac{6x^{2}-6-x}{6x}=0$$

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{6x^{2}-6-x}{6x}.

$$\frac{6\left(x-\left(-\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)\left(x-\left(\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)}{6x}=0$$

Cealaigh 6 mar uimhreoir agus ainmneoir.

$$\frac{\left(x-\left(-\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)\left(x-\left(\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)}{x}=0$$

Ní féidir leis an athróg x a bheith comhionann le 0 toisc nach bhfuil an roinnt faoi nialas sainithe. Méadaigh an dá thaobh den chothromóid faoi x.

$$\left(x-\left(-\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)\left(x-\left(\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)=0$$

Chun an mhalairt ar -\frac{1}{12}\sqrt{145}+\frac{1}{12} a aimsiú, aimsigh an mhalairt ar gach téarma.

$$\left(x-\left(-\frac{1}{12}\sqrt{145}\right)-\frac{1}{12}\right)\left(x-\left(\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)=0$$

Tá \frac{1}{12}\sqrt{145} urchomhairleach le -\frac{1}{12}\sqrt{145}.

$$\left(x+\frac{1}{12}\sqrt{145}-\frac{1}{12}\right)\left(x-\left(\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)=0$$

Chun an mhalairt ar \frac{1}{12}\sqrt{145}+\frac{1}{12} a aimsiú, aimsigh an mhalairt ar gach téarma.

$$\left(x+\frac{1}{12}\sqrt{145}-\frac{1}{12}\right)\left(x-\frac{1}{12}\sqrt{145}-\frac{1}{12}\right)=0$$

Cuir an t-airí dáileacháin i bhfeidhm trí gach téarma de x+\frac{1}{12}\sqrt{145}-\frac{1}{12} a iolrú faoi gach téarma de x-\frac{1}{12}\sqrt{145}-\frac{1}{12}.

$$x^{2}+x\left(-\frac{1}{12}\right)\sqrt{145}+x\left(-\frac{1}{12}\right)+\frac{1}{12}\sqrt{145}x+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)\sqrt{145}+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Méadaigh \sqrt{145} agus \sqrt{145} chun 145 a fháil.

$$x^{2}+x\left(-\frac{1}{12}\right)\sqrt{145}+x\left(-\frac{1}{12}\right)+\frac{1}{12}\sqrt{145}x+\frac{1}{12}\times 145\left(-\frac{1}{12}\right)+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Comhcheangail x\left(-\frac{1}{12}\right)\sqrt{145} agus \frac{1}{12}\sqrt{145}x chun 0 a fháil.

$$x^{2}+x\left(-\frac{1}{12}\right)+\frac{1}{12}\times 145\left(-\frac{1}{12}\right)+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Méadaigh \frac{1}{12} agus 145 chun \frac{145}{12} a fháil.

$$x^{2}+x\left(-\frac{1}{12}\right)+\frac{145}{12}\left(-\frac{1}{12}\right)+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Méadaigh \frac{145}{12} faoi -\frac{1}{12} tríd an uimhreoir a mhéadú faoin uimhreoir agus an t-ainmneoir a mhéadú faoin ainmneoir.

$$x^{2}+x\left(-\frac{1}{12}\right)+\frac{145\left(-1\right)}{12\times 12}+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Déan na hiolrúcháin sa chodán \frac{145\left(-1\right)}{12\times 12}.

$$x^{2}+x\left(-\frac{1}{12}\right)+\frac{-145}{144}+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Is féidir an codán \frac{-145}{144} a athscríobh mar -\frac{145}{144} ach an comhartha diúltach a bhaint.

$$x^{2}+x\left(-\frac{1}{12}\right)-\frac{145}{144}+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Méadaigh \frac{1}{12} faoi -\frac{1}{12} tríd an uimhreoir a mhéadú faoin uimhreoir agus an t-ainmneoir a mhéadú faoin ainmneoir.

$$x^{2}+x\left(-\frac{1}{12}\right)-\frac{145}{144}+\frac{1\left(-1\right)}{12\times 12}\sqrt{145}-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Déan na hiolrúcháin sa chodán \frac{1\left(-1\right)}{12\times 12}.

$$x^{2}+x\left(-\frac{1}{12}\right)-\frac{145}{144}+\frac{-1}{144}\sqrt{145}-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Is féidir an codán \frac{-1}{144} a athscríobh mar -\frac{1}{144} ach an comhartha diúltach a bhaint.

$$x^{2}+x\left(-\frac{1}{12}\right)-\frac{145}{144}-\frac{1}{144}\sqrt{145}-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Comhcheangail x\left(-\frac{1}{12}\right) agus -\frac{1}{12}x chun -\frac{1}{6}x a fháil.

$$x^{2}-\frac{1}{6}x-\frac{145}{144}-\frac{1}{144}\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Méadaigh -\frac{1}{12} faoi -\frac{1}{12} tríd an uimhreoir a mhéadú faoin uimhreoir agus an t-ainmneoir a mhéadú faoin ainmneoir.

$$x^{2}-\frac{1}{6}x-\frac{145}{144}-\frac{1}{144}\sqrt{145}+\frac{-\left(-1\right)}{12\times 12}\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Déan na hiolrúcháin sa chodán \frac{-\left(-1\right)}{12\times 12}.

$$x^{2}-\frac{1}{6}x-\frac{145}{144}-\frac{1}{144}\sqrt{145}+\frac{1}{144}\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Comhcheangail -\frac{1}{144}\sqrt{145} agus \frac{1}{144}\sqrt{145} chun 0 a fháil.

$$x^{2}-\frac{1}{6}x-\frac{145}{144}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Méadaigh -\frac{1}{12} faoi -\frac{1}{12} tríd an uimhreoir a mhéadú faoin uimhreoir agus an t-ainmneoir a mhéadú faoin ainmneoir.

$$x^{2}-\frac{1}{6}x-\frac{145}{144}+\frac{-\left(-1\right)}{12\times 12}=0$$

Déan na hiolrúcháin sa chodán \frac{-\left(-1\right)}{12\times 12}.

$$x^{2}-\frac{1}{6}x-\frac{145}{144}+\frac{1}{144}=0$$

Tá an t-ainmneoir céanna ag -\frac{145}{144} agus \frac{1}{144} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$x^{2}-\frac{1}{6}x+\frac{-145+1}{144}=0$$

Suimigh -145 agus 1 chun -144 a fháil.

$$x^{2}-\frac{1}{6}x+\frac{-144}{144}=0$$

Roinn -144 faoi 144 chun -1 a fháil.

$$x^{2}-\frac{1}{6}x-1=0$$

Tá an chothromóid seo i bhfoirm chaighdeánach: ax^{2}+bx+c=0. Cuir 1 in ionad a, -\frac{1}{6} in ionad b, agus -1 in ionad c san fhoirmle chearnach, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{1}{6}\right)±\sqrt{\left(-\frac{1}{6}\right)^{2}-4\left(-1\right)}}{2}$$

Cearnaigh -\frac{1}{6} trí uimhreoir agus ainmneoir an chodáin a chearnú.

$$x=\frac{-\left(-\frac{1}{6}\right)±\sqrt{\frac{1}{36}-4\left(-1\right)}}{2}$$

Méadaigh -4 faoi -1.

$$x=\frac{-\left(-\frac{1}{6}\right)±\sqrt{\frac{1}{36}+4}}{2}$$

Suimigh \frac{1}{36} le 4?

$$x=\frac{-\left(-\frac{1}{6}\right)±\sqrt{\frac{145}{36}}}{2}$$

Tóg fréamh chearnach \frac{145}{36}.

$$x=\frac{-\left(-\frac{1}{6}\right)±\frac{\sqrt{145}}{6}}{2}$$

Tá \frac{1}{6} urchomhairleach le -\frac{1}{6}.

$$x=\frac{\frac{1}{6}±\frac{\sqrt{145}}{6}}{2}$$

Réitigh an chothromóid x=\frac{\frac{1}{6}±\frac{\sqrt{145}}{6}}{2} nuair is ionann ± agus plus. Suimigh \frac{1}{6} le \frac{\sqrt{145}}{6}?

$$x=\frac{\sqrt{145}+1}{2\times 6}$$

Roinn \frac{1+\sqrt{145}}{6} faoi 2.

$$x=\frac{\sqrt{145}+1}{12}$$

Réitigh an chothromóid x=\frac{\frac{1}{6}±\frac{\sqrt{145}}{6}}{2} nuair is ionann ± agus míneas. Dealaigh \frac{\sqrt{145}}{6} ó \frac{1}{6}.

$$x=\frac{1-\sqrt{145}}{2\times 6}$$

Roinn \frac{1-\sqrt{145}}{6} faoi 2.

$$x=\frac{1-\sqrt{145}}{12}$$

Tá an chothromóid réitithe anois.

$$x=\frac{\sqrt{145}+1}{12} x=\frac{1-\sqrt{145}}{12}$$

Céimeanna chun an Chearnóg a Chomhlánú

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de x agus 6 ná 6x. Méadaigh \frac{1}{x} faoi \frac{6}{6}. Méadaigh \frac{1}{6} faoi \frac{x}{x}.

$$x=\frac{6}{6x}+\frac{x}{6x}$$

Tá an t-ainmneoir céanna ag \frac{6}{6x} agus \frac{x}{6x} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$x=\frac{6+x}{6x}$$

Bain \frac{6+x}{6x} ón dá thaobh.

$$x-\frac{6+x}{6x}=0$$

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Méadaigh x faoi \frac{6x}{6x}.

$$\frac{x\times 6x}{6x}-\frac{6+x}{6x}=0$$

Tá an t-ainmneoir céanna ag \frac{x\times 6x}{6x} agus \frac{6+x}{6x} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$\frac{x\times 6x-\left(6+x\right)}{6x}=0$$

Déan iolrúcháin in x\times 6x-\left(6+x\right).

$$\frac{6x^{2}-6-x}{6x}=0$$

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{6x^{2}-6-x}{6x}.

$$\frac{6\left(x-\left(-\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)\left(x-\left(\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)}{6x}=0$$

Cealaigh 6 mar uimhreoir agus ainmneoir.

$$\frac{\left(x-\left(-\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)\left(x-\left(\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)}{x}=0$$

Ní féidir leis an athróg x a bheith comhionann le 0 toisc nach bhfuil an roinnt faoi nialas sainithe. Méadaigh an dá thaobh den chothromóid faoi x.

$$\left(x-\left(-\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)\left(x-\left(\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)=0$$

Chun an mhalairt ar -\frac{1}{12}\sqrt{145}+\frac{1}{12} a aimsiú, aimsigh an mhalairt ar gach téarma.

$$\left(x-\left(-\frac{1}{12}\sqrt{145}\right)-\frac{1}{12}\right)\left(x-\left(\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)=0$$

Tá \frac{1}{12}\sqrt{145} urchomhairleach le -\frac{1}{12}\sqrt{145}.

$$\left(x+\frac{1}{12}\sqrt{145}-\frac{1}{12}\right)\left(x-\left(\frac{1}{12}\sqrt{145}+\frac{1}{12}\right)\right)=0$$

Chun an mhalairt ar \frac{1}{12}\sqrt{145}+\frac{1}{12} a aimsiú, aimsigh an mhalairt ar gach téarma.

$$\left(x+\frac{1}{12}\sqrt{145}-\frac{1}{12}\right)\left(x-\frac{1}{12}\sqrt{145}-\frac{1}{12}\right)=0$$

Cuir an t-airí dáileacháin i bhfeidhm trí gach téarma de x+\frac{1}{12}\sqrt{145}-\frac{1}{12} a iolrú faoi gach téarma de x-\frac{1}{12}\sqrt{145}-\frac{1}{12}.

$$x^{2}+x\left(-\frac{1}{12}\right)\sqrt{145}+x\left(-\frac{1}{12}\right)+\frac{1}{12}\sqrt{145}x+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)\sqrt{145}+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Méadaigh \sqrt{145} agus \sqrt{145} chun 145 a fháil.

$$x^{2}+x\left(-\frac{1}{12}\right)\sqrt{145}+x\left(-\frac{1}{12}\right)+\frac{1}{12}\sqrt{145}x+\frac{1}{12}\times 145\left(-\frac{1}{12}\right)+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Comhcheangail x\left(-\frac{1}{12}\right)\sqrt{145} agus \frac{1}{12}\sqrt{145}x chun 0 a fháil.

$$x^{2}+x\left(-\frac{1}{12}\right)+\frac{1}{12}\times 145\left(-\frac{1}{12}\right)+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Méadaigh \frac{1}{12} agus 145 chun \frac{145}{12} a fháil.

$$x^{2}+x\left(-\frac{1}{12}\right)+\frac{145}{12}\left(-\frac{1}{12}\right)+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Méadaigh \frac{145}{12} faoi -\frac{1}{12} tríd an uimhreoir a mhéadú faoin uimhreoir agus an t-ainmneoir a mhéadú faoin ainmneoir.

$$x^{2}+x\left(-\frac{1}{12}\right)+\frac{145\left(-1\right)}{12\times 12}+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Déan na hiolrúcháin sa chodán \frac{145\left(-1\right)}{12\times 12}.

$$x^{2}+x\left(-\frac{1}{12}\right)+\frac{-145}{144}+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Is féidir an codán \frac{-145}{144} a athscríobh mar -\frac{145}{144} ach an comhartha diúltach a bhaint.

$$x^{2}+x\left(-\frac{1}{12}\right)-\frac{145}{144}+\frac{1}{12}\sqrt{145}\left(-\frac{1}{12}\right)-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Méadaigh \frac{1}{12} faoi -\frac{1}{12} tríd an uimhreoir a mhéadú faoin uimhreoir agus an t-ainmneoir a mhéadú faoin ainmneoir.

$$x^{2}+x\left(-\frac{1}{12}\right)-\frac{145}{144}+\frac{1\left(-1\right)}{12\times 12}\sqrt{145}-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Déan na hiolrúcháin sa chodán \frac{1\left(-1\right)}{12\times 12}.

$$x^{2}+x\left(-\frac{1}{12}\right)-\frac{145}{144}+\frac{-1}{144}\sqrt{145}-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Is féidir an codán \frac{-1}{144} a athscríobh mar -\frac{1}{144} ach an comhartha diúltach a bhaint.

$$x^{2}+x\left(-\frac{1}{12}\right)-\frac{145}{144}-\frac{1}{144}\sqrt{145}-\frac{1}{12}x-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Comhcheangail x\left(-\frac{1}{12}\right) agus -\frac{1}{12}x chun -\frac{1}{6}x a fháil.

$$x^{2}-\frac{1}{6}x-\frac{145}{144}-\frac{1}{144}\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Méadaigh -\frac{1}{12} faoi -\frac{1}{12} tríd an uimhreoir a mhéadú faoin uimhreoir agus an t-ainmneoir a mhéadú faoin ainmneoir.

$$x^{2}-\frac{1}{6}x-\frac{145}{144}-\frac{1}{144}\sqrt{145}+\frac{-\left(-1\right)}{12\times 12}\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Déan na hiolrúcháin sa chodán \frac{-\left(-1\right)}{12\times 12}.

$$x^{2}-\frac{1}{6}x-\frac{145}{144}-\frac{1}{144}\sqrt{145}+\frac{1}{144}\sqrt{145}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Comhcheangail -\frac{1}{144}\sqrt{145} agus \frac{1}{144}\sqrt{145} chun 0 a fháil.

$$x^{2}-\frac{1}{6}x-\frac{145}{144}-\frac{1}{12}\left(-\frac{1}{12}\right)=0$$

Méadaigh -\frac{1}{12} faoi -\frac{1}{12} tríd an uimhreoir a mhéadú faoin uimhreoir agus an t-ainmneoir a mhéadú faoin ainmneoir.

$$x^{2}-\frac{1}{6}x-\frac{145}{144}+\frac{-\left(-1\right)}{12\times 12}=0$$

Déan na hiolrúcháin sa chodán \frac{-\left(-1\right)}{12\times 12}.

$$x^{2}-\frac{1}{6}x-\frac{145}{144}+\frac{1}{144}=0$$

Tá an t-ainmneoir céanna ag -\frac{145}{144} agus \frac{1}{144} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$x^{2}-\frac{1}{6}x+\frac{-145+1}{144}=0$$

Suimigh -145 agus 1 chun -144 a fháil.

$$x^{2}-\frac{1}{6}x+\frac{-144}{144}=0$$

Roinn -144 faoi 144 chun -1 a fháil.

$$x^{2}-\frac{1}{6}x-1=0$$

Cuir 1 leis an dá thaobh. Is ionann rud ar bith móide nialas agus a shuim féin.

$$x^{2}-\frac{1}{6}x=1$$

Roinn -\frac{1}{6}, comhéifeacht an téarma x, faoi 2 chun -\frac{1}{12} a fháil. Ansin suimigh uimhir chearnach -\frac{1}{12} leis an dá thaobh den chothromóid. Déanann an chéim seo slánchearnóg de thaobh clé na cothromóide.

$$x^{2}-\frac{1}{6}x+\left(-\frac{1}{12}\right)^{2}=1+\left(-\frac{1}{12}\right)^{2}$$

Cearnaigh -\frac{1}{12} trí uimhreoir agus ainmneoir an chodáin a chearnú.

$$x^{2}-\frac{1}{6}x+\frac{1}{144}=1+\frac{1}{144}$$

Suimigh 1 le \frac{1}{144}?

$$x^{2}-\frac{1}{6}x+\frac{1}{144}=\frac{145}{144}$$

Fachtóirigh x^{2}-\frac{1}{6}x+\frac{1}{144}. Go ginearálta, nuair x^{2}+bx+c cearnóg fhoirfe é, is féidir é a fhachtóiriú i gcónaí mar \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{1}{12}\right)^{2}=\frac{145}{144}$$

Tóg fréamh chearnach an dá thaobh den chothromóid.

$$\sqrt{\left(x-\frac{1}{12}\right)^{2}}=\sqrt{\frac{145}{144}}$$

Simpligh.

$$x-\frac{1}{12}=\frac{\sqrt{145}}{12} x-\frac{1}{12}=-\frac{\sqrt{145}}{12}$$

Cuir \frac{1}{12} leis an dá thaobh den chothromóid.

$$x=\frac{\sqrt{145}+1}{12} x=\frac{1-\sqrt{145}}{12}$$