Réitigh 5/w^2-32=6/w^2+56

$$\frac { 5 } { w ^ { 2 } } - 32 = \frac { 6 } { w ^ { 2 } } + 56$$

Réitigh do w.

$$w=-\frac{\sqrt{22}i}{44}\approx -0-0.106600358i$$

$$w=\frac{\sqrt{22}i}{44}\approx 0.106600358i$$

Céimeanna tríd an bhFréamh Chearnach a Fháil

Ní féidir leis an athróg w a bheith comhionann le 0 toisc nach bhfuil an roinnt faoi nialas sainithe. Méadaigh an dá thaobh den chothromóid faoi w^{2}.

$$5+w^{2}\left(-32\right)=6+w^{2}\times 56$$

Bain w^{2}\times 56 ón dá thaobh.

$$5+w^{2}\left(-32\right)-w^{2}\times 56=6$$

Comhcheangail w^{2}\left(-32\right) agus -w^{2}\times 56 chun -88w^{2} a fháil.

$$5-88w^{2}=6$$

Bain 5 ón dá thaobh.

$$-88w^{2}=6-5$$

Dealaigh 5 ó 6 chun 1 a fháil.

$$-88w^{2}=1$$

Roinn an dá thaobh faoi -88.

$$w^{2}=-\frac{1}{88}$$

Tá an chothromóid réitithe anois.

$$w=\frac{\sqrt{22}i}{44} w=-\frac{\sqrt{22}i}{44}$$

Céimeanna ag Baint Úsáid as an bhFoirmle Chearnach

Ní féidir leis an athróg w a bheith comhionann le 0 toisc nach bhfuil an roinnt faoi nialas sainithe. Méadaigh an dá thaobh den chothromóid faoi w^{2}.

$$5+w^{2}\left(-32\right)=6+w^{2}\times 56$$

Bain 6 ón dá thaobh.

$$5+w^{2}\left(-32\right)-6=w^{2}\times 56$$

Dealaigh 6 ó 5 chun -1 a fháil.

$$-1+w^{2}\left(-32\right)=w^{2}\times 56$$

Bain w^{2}\times 56 ón dá thaobh.

$$-1+w^{2}\left(-32\right)-w^{2}\times 56=0$$

Comhcheangail w^{2}\left(-32\right) agus -w^{2}\times 56 chun -88w^{2} a fháil.

$$-1-88w^{2}=0$$

Is féidir cothromóidí cearnacha cosúil leis an gceann seo, le téarma x^{2} ach gan téarma x, a réiteach fós ag baint úsáid as an bhfoirmle chearnach, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, nuair a chuirfear i bhfoirm chaighdeánach iad: ax^{2}+bx+c=0.

$$-88w^{2}-1=0$$

Tá an chothromóid seo i bhfoirm chaighdeánach: ax^{2}+bx+c=0. Cuir -88 in ionad a, 0 in ionad b, agus -1 in ionad c san fhoirmle chearnach, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{0±\sqrt{0^{2}-4\left(-88\right)\left(-1\right)}}{2\left(-88\right)}$$

Cearnóg 0.

$$w=\frac{0±\sqrt{-4\left(-88\right)\left(-1\right)}}{2\left(-88\right)}$$

Méadaigh -4 faoi -88.

$$w=\frac{0±\sqrt{352\left(-1\right)}}{2\left(-88\right)}$$

Méadaigh 352 faoi -1.

$$w=\frac{0±\sqrt{-352}}{2\left(-88\right)}$$

Tóg fréamh chearnach -352.

$$w=\frac{0±4\sqrt{22}i}{2\left(-88\right)}$$

Méadaigh 2 faoi -88.

$$w=\frac{0±4\sqrt{22}i}{-176}$$

Réitigh an chothromóid w=\frac{0±4\sqrt{22}i}{-176} nuair is ionann ± agus plus.

$$w=-\frac{\sqrt{22}i}{44}$$

Réitigh an chothromóid w=\frac{0±4\sqrt{22}i}{-176} nuair is ionann ± agus míneas.

$$w=\frac{\sqrt{22}i}{44}$$

Tá an chothromóid réitithe anois.

$$w=-\frac{\sqrt{22}i}{44} w=\frac{\sqrt{22}i}{44}$$