Réitigh 5-x/4*10^6=96x-x^2

$$\frac { 5 - x } { 4 \times 10 ^ { 6 } } = 96 x - x ^ { 2 }$$

Réitigh do x.

$$x = \frac{\sqrt{147456000688000001} + 384000001}{8000000} \approx 96.000000237$$

$$x=\frac{384000001-\sqrt{147456000688000001}}{8000000}\approx 0.000000013$$

Céimeanna ag Baint Úsáid as an bhFoirmle Chearnach

Ríomh cumhacht 10 de 6 agus faigh 1000000.

$$\frac{5-x}{4\times 1000000}=96x-x^{2}$$

Méadaigh 4 agus 1000000 chun 4000000 a fháil.

$$\frac{5-x}{4000000}=96x-x^{2}$$

Roinn 5-x faoi 4000000 chun \frac{1}{800000}-\frac{1}{4000000}x a fháil.

$$\frac{1}{800000}-\frac{1}{4000000}x=96x-x^{2}$$

Bain 96x ón dá thaobh.

$$\frac{1}{800000}-\frac{1}{4000000}x-96x=-x^{2}$$

Comhcheangail -\frac{1}{4000000}x agus -96x chun -\frac{384000001}{4000000}x a fháil.

$$\frac{1}{800000}-\frac{384000001}{4000000}x=-x^{2}$$

Cuir x^{2} leis an dá thaobh.

$$\frac{1}{800000}-\frac{384000001}{4000000}x+x^{2}=0$$

Is féidir gach cothromóid san fhoirm ax^{2}+bx+c=0 a réiteach ag baint úsáid as an bhfoirmle chearnach : \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Tugann an fhoirmle chearnach dhá réiteach, ceann amháin nuair is suimiú é ± agus ceann eile nuair is dealú é.

$$x^{2}-\frac{384000001}{4000000}x+\frac{1}{800000}=0$$

Tá an chothromóid seo i bhfoirm chaighdeánach: ax^{2}+bx+c=0. Cuir 1 in ionad a, -\frac{384000001}{4000000} in ionad b, agus \frac{1}{800000} in ionad c san fhoirmle chearnach, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{384000001}{4000000}\right)±\sqrt{\left(-\frac{384000001}{4000000}\right)^{2}-4\times \frac{1}{800000}}}{2}$$

Cearnaigh -\frac{384000001}{4000000} trí uimhreoir agus ainmneoir an chodáin a chearnú.

$$x=\frac{-\left(-\frac{384000001}{4000000}\right)±\sqrt{\frac{147456000768000001}{16000000000000}-4\times \frac{1}{800000}}}{2}$$

Méadaigh -4 faoi \frac{1}{800000}.

$$x=\frac{-\left(-\frac{384000001}{4000000}\right)±\sqrt{\frac{147456000768000001}{16000000000000}-\frac{1}{200000}}}{2}$$

Suimigh \frac{147456000768000001}{16000000000000} le -\frac{1}{200000} trí chomhainmneoir a fháil agus na huimhreoirí a shuimiú. Laghdaigh an codán ansin go dtí na téarmaí is ísle más féidir.

$$x=\frac{-\left(-\frac{384000001}{4000000}\right)±\sqrt{\frac{147456000688000001}{16000000000000}}}{2}$$

Tóg fréamh chearnach \frac{147456000688000001}{16000000000000}.

$$x=\frac{-\left(-\frac{384000001}{4000000}\right)±\frac{\sqrt{147456000688000001}}{4000000}}{2}$$

Tá \frac{384000001}{4000000} urchomhairleach le -\frac{384000001}{4000000}.

$$x=\frac{\frac{384000001}{4000000}±\frac{\sqrt{147456000688000001}}{4000000}}{2}$$

Réitigh an chothromóid x=\frac{\frac{384000001}{4000000}±\frac{\sqrt{147456000688000001}}{4000000}}{2} nuair is ionann ± agus plus. Suimigh \frac{384000001}{4000000} le \frac{\sqrt{147456000688000001}}{4000000}?

$$x=\frac{\sqrt{147456000688000001}[phone]}{2\times 4000000}$$

Roinn \frac{384000001+\sqrt{147456000688000001}}{4000000} faoi 2.

$$x=\frac{\sqrt{147456000688000001}[phone]}{8000000}$$

Réitigh an chothromóid x=\frac{\frac{384000001}{4000000}±\frac{\sqrt{147456000688000001}}{4000000}}{2} nuair is ionann ± agus míneas. Dealaigh \frac{\sqrt{147456000688000001}}{4000000} ó \frac{384000001}{4000000}.

$$x=\frac{384000001-\sqrt{147456000688000001}}{2\times 4000000}$$

Roinn \frac{384000001-\sqrt{147456000688000001}}{4000000} faoi 2.

$$x=\frac{384000001-\sqrt{147456000688000001}}{8000000}$$

Tá an chothromóid réitithe anois.

$$x=\frac{\sqrt{147456000688000001}[phone]}{8000000} x=\frac{384000001-\sqrt{147456000688000001}}{8000000}$$

Céimeanna chun an Chearnóg a Chomhlánú

Ríomh cumhacht 10 de 6 agus faigh 1000000.

$$\frac{5-x}{4\times 1000000}=96x-x^{2}$$

Méadaigh 4 agus 1000000 chun 4000000 a fháil.

$$\frac{5-x}{4000000}=96x-x^{2}$$

Roinn 5-x faoi 4000000 chun \frac{1}{800000}-\frac{1}{4000000}x a fháil.

$$\frac{1}{800000}-\frac{1}{4000000}x=96x-x^{2}$$

Bain 96x ón dá thaobh.

$$\frac{1}{800000}-\frac{1}{4000000}x-96x=-x^{2}$$

Comhcheangail -\frac{1}{4000000}x agus -96x chun -\frac{384000001}{4000000}x a fháil.

$$\frac{1}{800000}-\frac{384000001}{4000000}x=-x^{2}$$

Cuir x^{2} leis an dá thaobh.

$$\frac{1}{800000}-\frac{384000001}{4000000}x+x^{2}=0$$

Bain \frac{1}{800000} ón dá thaobh. Is ionann rud ar bith a dhealaítear ó nialas agus a shéanadh.

$$-\frac{384000001}{4000000}x+x^{2}=-\frac{1}{800000}$$

Is féidir cothromóidí cearnach cosúil leis an gceann seo a réitigh tríd an gcearnóg a chomhlánú. Chun an chearnóg a chomhlánú, ní mór don chothromóid a bheith san fhoirm x^{2}+bx=c ar dtús.

$$x^{2}-\frac{384000001}{4000000}x=-\frac{1}{800000}$$

Roinn -\frac{384000001}{4000000}, comhéifeacht an téarma x, faoi 2 chun -\frac{384000001}{8000000} a fháil. Ansin suimigh uimhir chearnach -\frac{384000001}{8000000} leis an dá thaobh den chothromóid. Déanann an chéim seo slánchearnóg de thaobh clé na cothromóide.

$$x^{2}-\frac{384000001}{4000000}x+\left(-\frac{384000001}{8000000}\right)^{2}=-\frac{1}{800000}+\left(-\frac{384000001}{8000000}\right)^{2}$$

Cearnaigh -\frac{384000001}{8000000} trí uimhreoir agus ainmneoir an chodáin a chearnú.

$$x^{2}-\frac{384000001}{4000000}x+\frac{147456000768000001}{64000000000000}=-\frac{1}{800000}+\frac{147456000768000001}{64000000000000}$$

Suimigh -\frac{1}{800000} le \frac{147456000768000001}{64000000000000} trí chomhainmneoir a fháil agus na huimhreoirí a shuimiú. Laghdaigh an codán ansin go dtí na téarmaí is ísle más féidir.

$$x^{2}-\frac{384000001}{4000000}x+\frac{147456000768000001}{64000000000000}=\frac{147456000688000001}{64000000000000}$$

Fachtóirigh x^{2}-\frac{384000001}{4000000}x+\frac{147456000768000001}{64000000000000}. 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}.

$$\left(x-\frac{384000001}{8000000}\right)^{2}=\frac{147456000688000001}{64000000000000}$$

Tóg fréamh chearnach an dá thaobh den chothromóid.

$$\sqrt{\left(x-\frac{384000001}{8000000}\right)^{2}}=\sqrt{\frac{147456000688000001}{64000000000000}}$$

Simpligh.

$$x-\frac{384000001}{8000000}=\frac{\sqrt{147456000688000001}}{8000000} x-\frac{384000001}{8000000}=-\frac{\sqrt{147456000688000001}}{8000000}$$

Cuir \frac{384000001}{8000000} leis an dá thaobh den chothromóid.

$$x=\frac{\sqrt{147456000688000001}[phone]}{8000000} x=\frac{384000001-\sqrt{147456000688000001}}{8000000}$$