Réitigh a^2+(4a+10)^2=64/25

$$a ^ { 2 } + ( 4 a + 10 ) ^ { 2 } = \frac { 64 } { 25 }$$

Réitigh do a.

$$a=\frac{2\sqrt{353}i}{85}-\frac{40}{17}\approx -2.352941176+0.442077511i$$

$$a=-\frac{2\sqrt{353}i}{85}-\frac{40}{17}\approx -2.352941176-0.442077511i$$

Céimeanna ag Baint Úsáid as an bhFoirmle Chearnach

Úsáid an teoirim dhéthéarmach \left(a+b\right)^{2}=a^{2}+2ab+b^{2} chun \left(4a+10\right)^{2} a leathnú.

$$a^{2}+16a^{2}+80a+100=\frac{64}{25}$$

Comhcheangail a^{2} agus 16a^{2} chun 17a^{2} a fháil.

$$17a^{2}+80a+100=\frac{64}{25}$$

Bain \frac{64}{25} ón dá thaobh.

$$17a^{2}+80a+100-\frac{64}{25}=0$$

Dealaigh \frac{64}{25} ó 100 chun \frac{2436}{25} a fháil.

$$17a^{2}+80a+\frac{2436}{25}=0$$

Tá an chothromóid seo i bhfoirm chaighdeánach: ax^{2}+bx+c=0. Cuir 17 in ionad a, 80 in ionad b, agus \frac{2436}{25} in ionad c san fhoirmle chearnach, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{-80±\sqrt{80^{2}-4\times 17\times \frac{2436}{25}}}{2\times 17}$$

Cearnóg 80.

$$a=\frac{-80±\sqrt{6400-4\times 17\times \frac{2436}{25}}}{2\times 17}$$

Méadaigh -4 faoi 17.

$$a=\frac{-80±\sqrt{6400-68\times \frac{2436}{25}}}{2\times 17}$$

Méadaigh -68 faoi \frac{2436}{25}.

$$a=\frac{-80±\sqrt{6400-\frac{165648}{25}}}{2\times 17}$$

Suimigh 6400 le -\frac{165648}{25}?

$$a=\frac{-80±\sqrt{-\frac{5648}{25}}}{2\times 17}$$

Tóg fréamh chearnach -\frac{5648}{25}.

$$a=\frac{-80±\frac{4\sqrt{353}i}{5}}{2\times 17}$$

Méadaigh 2 faoi 17.

$$a=\frac{-80±\frac{4\sqrt{353}i}{5}}{34}$$

Réitigh an chothromóid a=\frac{-80±\frac{4\sqrt{353}i}{5}}{34} nuair is ionann ± agus plus. Suimigh -80 le \frac{4i\sqrt{353}}{5}?

$$a=\frac{\frac{4\sqrt{353}i}{5}-80}{34}$$

Roinn -80+\frac{4i\sqrt{353}}{5} faoi 34.

$$a=\frac{2\sqrt{353}i}{85}-\frac{40}{17}$$

Réitigh an chothromóid a=\frac{-80±\frac{4\sqrt{353}i}{5}}{34} nuair is ionann ± agus míneas. Dealaigh \frac{4i\sqrt{353}}{5} ó -80.

$$a=\frac{-\frac{4\sqrt{353}i}{5}-80}{34}$$

Roinn -80-\frac{4i\sqrt{353}}{5} faoi 34.

$$a=-\frac{2\sqrt{353}i}{85}-\frac{40}{17}$$

Tá an chothromóid réitithe anois.

$$a=\frac{2\sqrt{353}i}{85}-\frac{40}{17} a=-\frac{2\sqrt{353}i}{85}-\frac{40}{17}$$

Céimeanna chun an Chearnóg a Chomhlánú

Úsáid an teoirim dhéthéarmach \left(a+b\right)^{2}=a^{2}+2ab+b^{2} chun \left(4a+10\right)^{2} a leathnú.

$$a^{2}+16a^{2}+80a+100=\frac{64}{25}$$

Comhcheangail a^{2} agus 16a^{2} chun 17a^{2} a fháil.

$$17a^{2}+80a+100=\frac{64}{25}$$

Bain 100 ón dá thaobh.

$$17a^{2}+80a=\frac{64}{25}-100$$

Dealaigh 100 ó \frac{64}{25} chun -\frac{2436}{25} a fháil.

$$17a^{2}+80a=-\frac{2436}{25}$$

Roinn an dá thaobh faoi 17.

$$\frac{17a^{2}+80a}{17}=-\frac{\frac{2436}{25}}{17}$$

Má roinntear é faoi 17 cuirtear an iolrúchán faoi 17 ar ceal.

$$a^{2}+\frac{80}{17}a=-\frac{\frac{2436}{25}}{17}$$

Roinn -\frac{2436}{25} faoi 17.

$$a^{2}+\frac{80}{17}a=-\frac{2436}{425}$$

Roinn \frac{80}{17}, comhéifeacht an téarma x, faoi 2 chun \frac{40}{17} a fháil. Ansin suimigh uimhir chearnach \frac{40}{17} leis an dá thaobh den chothromóid. Déanann an chéim seo slánchearnóg de thaobh clé na cothromóide.

$$a^{2}+\frac{80}{17}a+\left(\frac{40}{17}\right)^{2}=-\frac{2436}{425}+\left(\frac{40}{17}\right)^{2}$$

Cearnaigh \frac{40}{17} trí uimhreoir agus ainmneoir an chodáin a chearnú.

$$a^{2}+\frac{80}{17}a+\frac{1600}{289}=-\frac{2436}{425}+\frac{1600}{289}$$

Suimigh -\frac{2436}{425} le \frac{1600}{289} trí chomhainmneoir a fháil agus na huimhreoirí a shuimiú. Laghdaigh an codán ansin go dtí na téarmaí is ísle más féidir.

$$a^{2}+\frac{80}{17}a+\frac{1600}{289}=-\frac{1412}{7225}$$

Fachtóirigh a^{2}+\frac{80}{17}a+\frac{1600}{289}. 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}.

$$\left(a+\frac{40}{17}\right)^{2}=-\frac{1412}{7225}$$

Tóg fréamh chearnach an dá thaobh den chothromóid.

$$\sqrt{\left(a+\frac{40}{17}\right)^{2}}=\sqrt{-\frac{1412}{7225}}$$

Simpligh.

$$a+\frac{40}{17}=\frac{2\sqrt{353}i}{85} a+\frac{40}{17}=-\frac{2\sqrt{353}i}{85}$$

Bain \frac{40}{17} ón dá thaobh den chothromóid.

$$a=\frac{2\sqrt{353}i}{85}-\frac{40}{17} a=-\frac{2\sqrt{353}i}{85}-\frac{40}{17}$$