Réitigh 75n=68n-n^2+cos544-8n

$$75 n = 68 n - n ^ { 2 } + \cos 544 - 8 n$$

Réitigh do n.

$$n=\frac{\sqrt{552524359497401758}}{100000000}-7.5\approx -0.066801768$$

$$n=-\frac{\sqrt{552524359497401758}}{100000000}-7.5\approx -14.933198232$$

Céimeanna ag Baint Úsáid as an bhFoirmle Chearnach

Evaluate trigonometric functions in the problem

$$75 n = 68 n - n ^ {2} + -0.9975640502598242 - 8 n$$

Comhcheangail 68n agus -8n chun 60n a fháil.

$$75n=60n-n^{2}-0.9975640502598242$$

Bain 60n ón dá thaobh.

$$75n-60n=-n^{2}-0.9975640502598242$$

Comhcheangail 75n agus -60n chun 15n a fháil.

$$15n=-n^{2}-0.9975640502598242$$

Cuir n^{2} leis an dá thaobh.

$$15n+n^{2}=-0.9975640502598242$$

Cuir 0.9975640502598242 leis an dá thaobh.

$$15n+n^{2}+0.9975640502598242=0$$

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.

$$n^{2}+15n+0.9975640502598242=0$$

Tá an chothromóid seo i bhfoirm chaighdeánach: ax^{2}+bx+c=0. Cuir 1 in ionad a, 15 in ionad b, agus 0.9975640502598242 in ionad c san fhoirmle chearnach, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{-15±\sqrt{15^{2}-4\times 0.9975640502598242}}{2}$$

Cearnóg 15.

$$n=\frac{-15±\sqrt{225-4\times 0.9975640502598242}}{2}$$

Méadaigh -4 faoi 0.9975640502598242.

$$n=\frac{-15±\sqrt{225-3.9902562010392968}}{2}$$

Suimigh 225 le -3.9902562010392968?

$$n=\frac{-15±\sqrt{221.0097437989607032}}{2}$$

Tóg fréamh chearnach 221.0097437989607032.

$$n=\frac{-15±\frac{\sqrt{552524359497401758}}{50000000}}{2}$$

Réitigh an chothromóid n=\frac{-15±\frac{\sqrt{552524359497401758}}{50000000}}{2} nuair is ionann ± agus plus. Suimigh -15 le \frac{\sqrt{552524359497401758}}{50000000}?

$$n=\frac{\frac{\sqrt{552524359497401758}}{50000000}-15}{2}$$

Roinn -15+\frac{\sqrt{552524359497401758}}{50000000} faoi 2.

$$n=\frac{\sqrt{552524359497401758}}{100000000}-\frac{15}{2}$$

Réitigh an chothromóid n=\frac{-15±\frac{\sqrt{552524359497401758}}{50000000}}{2} nuair is ionann ± agus míneas. Dealaigh \frac{\sqrt{552524359497401758}}{50000000} ó -15.

$$n=\frac{-\frac{\sqrt{552524359497401758}}{50000000}-15}{2}$$

Roinn -15-\frac{\sqrt{552524359497401758}}{50000000} faoi 2.

$$n=-\frac{\sqrt{552524359497401758}}{100000000}-\frac{15}{2}$$

Tá an chothromóid réitithe anois.

$$n=\frac{\sqrt{552524359497401758}}{100000000}-\frac{15}{2} n=-\frac{\sqrt{552524359497401758}}{100000000}-\frac{15}{2}$$

Céimeanna chun an Chearnóg a Chomhlánú

Evaluate trigonometric functions in the problem

$$75 n = 68 n - n ^ {2} + -0.9975640502598242 - 8 n$$

Comhcheangail 68n agus -8n chun 60n a fháil.

$$75n=60n-n^{2}-0.9975640502598242$$

Bain 60n ón dá thaobh.

$$75n-60n=-n^{2}-0.9975640502598242$$

Comhcheangail 75n agus -60n chun 15n a fháil.

$$15n=-n^{2}-0.9975640502598242$$

Cuir n^{2} leis an dá thaobh.

$$15n+n^{2}=-0.9975640502598242$$

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.

$$n^{2}+15n=-0.9975640502598242$$

Roinn 15, comhéifeacht an téarma x, faoi 2 chun \frac{15}{2} a fháil. Ansin suimigh uimhir chearnach \frac{15}{2} leis an dá thaobh den chothromóid. Déanann an chéim seo slánchearnóg de thaobh clé na cothromóide.

$$n^{2}+15n+\left(\frac{15}{2}\right)^{2}=-0.9975640502598242+\left(\frac{15}{2}\right)^{2}$$

Cearnaigh \frac{15}{2} trí uimhreoir agus ainmneoir an chodáin a chearnú.

$$n^{2}+15n+\frac{225}{4}=-0.9975640502598242+\frac{225}{4}$$

Suimigh -0.9975640502598242 le \frac{225}{4} trí chomhainmneoir a fháil agus na huimhreoirí a shuimiú. Laghdaigh an codán ansin go dtí na téarmaí is ísle más féidir.

$$n^{2}+15n+\frac{225}{4}=\frac{276262179748700879}{5000000000000000}$$

Fachtóirigh n^{2}+15n+\frac{225}{4}. 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}.

$$\left(n+\frac{15}{2}\right)^{2}=\frac{276262179748700879}{5000000000000000}$$

Tóg fréamh chearnach an dá thaobh den chothromóid.

$$\sqrt{\left(n+\frac{15}{2}\right)^{2}}=\sqrt{\frac{276262179748700879}{5000000000000000}}$$

Simpligh.

$$n+\frac{15}{2}=\frac{\sqrt{552524359497401758}}{100000000} n+\frac{15}{2}=-\frac{\sqrt{552524359497401758}}{100000000}$$

Bain \frac{15}{2} ón dá thaobh den chothromóid.

$$n=\frac{\sqrt{552524359497401758}}{100000000}-\frac{15}{2} n=-\frac{\sqrt{552524359497401758}}{100000000}-\frac{15}{2}$$