Issolvi 473^-4=x^2/64-x

$${ 473 }^{ -4 } = \frac{ { x }^{ 2 } }{ 64-x }$$

Solvi għal x

$$x=\frac{\sqrt{12813994352897}-1}{100109330882}\approx 0.000035758$$

$$x=\frac{-\sqrt{12813994352897}-1}{100109330882}\approx -0.000035758$$

Passi għall-Użu tal-Formula Kwadratika

Il-varjabbli x ma jistax ikun ugwali għal 64 billi d-diviżjoni b'żero mhux iddefinit. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'-x+64.

$$\left(-x+64\right)\times 473^{-4}=x^{2}$$

Ikkalkula 473 bil-power ta' -4 u tikseb \frac{1}{50054665441}.

$$\left(-x+64\right)\times \frac{1}{50054665441}=x^{2}$$

Uża l-propjetà distributtiva biex timmultiplika -x+64 b'\frac{1}{50054665441}.

$$-\frac{1}{50054665441}x+\frac{64}{50054665441}=x^{2}$$

Naqqas x^{2} miż-żewġ naħat.

$$-\frac{1}{50054665441}x+\frac{64}{50054665441}-x^{2}=0$$

L-ekwazzjonijiet kollha tal-formola ax^{2}+bx+c=0 jistgħu jiġu solvuti permezz tal-formula kwadratika: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Il-formula kwadratika tagħti żewġ soluzzjonijiet, waħda meta ± hija addizzjoni u waħda meta hija tnaqqis.

$$-x^{2}-\frac{1}{50054665441}x+\frac{64}{50054665441}=0$$

Din l-ekwazzjoni hija fil-forma standard: ax^{2}+bx+c=0. Issostitwixxi -1 għal a, -\frac{1}{50054665441} għal b, u \frac{64}{50054665441} għal c fil-formula kwadratika, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{1}{50054665441}\right)±\sqrt{\left(-\frac{1}{50054665441}\right)^{2}-4\left(-1\right)\times \frac{64}{50054665441}}}{2\left(-1\right)}$$

Ikkwadra -\frac{1}{50054665441} billi tikkwadra kemm in-numeratur u d-denominatur tal-frazzjoni.

$$x=\frac{-\left(-\frac{1}{50054665441}\right)±\sqrt{\frac{1}{2505469532410439724481}-4\left(-1\right)\times \frac{64}{50054665441}}}{2\left(-1\right)}$$

Immultiplika -4 b'-1.

$$x=\frac{-\left(-\frac{1}{50054665441}\right)±\sqrt{\frac{1}{2505469532410439724481}+4\times \frac{64}{50054665441}}}{2\left(-1\right)}$$

Immultiplika 4 b'\frac{64}{50054665441}.

$$x=\frac{-\left(-\frac{1}{50054665441}\right)±\sqrt{\frac{1}{2505469532410439724481}+\frac{256}{50054665441}}}{2\left(-1\right)}$$

Żid \frac{1}{2505469532410439724481} ma' \frac{256}{50054665441} biex issib id-denominatur komuni u żżid in-numeraturi. Imbagħad naqqas il-frazzjoni għat-termini l-aktar baxxi jekk possibbli.

$$x=\frac{-\left(-\frac{1}{50054665441}\right)±\sqrt{\frac{12813994352897}{2505469532410439724481}}}{2\left(-1\right)}$$

Ħu l-għerq kwadrat ta' \frac{12813994352897}{2505469532410439724481}.

$$x=\frac{-\left(-\frac{1}{50054665441}\right)±\frac{\sqrt{12813994352897}}{50054665441}}{2\left(-1\right)}$$

L-oppost ta' -\frac{1}{50054665441} huwa \frac{1}{50054665441}.

$$x=\frac{\frac{1}{50054665441}±\frac{\sqrt{12813994352897}}{50054665441}}{2\left(-1\right)}$$

Immultiplika 2 b'-1.

$$x=\frac{\frac{1}{50054665441}±\frac{\sqrt{12813994352897}}{50054665441}}{-2}$$

Issa solvi l-ekwazzjoni x=\frac{\frac{1}{50054665441}±\frac{\sqrt{12813994352897}}{50054665441}}{-2} fejn ± hija plus. Żid \frac{1}{50054665441} ma' \frac{\sqrt{12813994352897}}{50054665441}.

$$x=\frac{\sqrt{12813994352897}+1}{-2\times 50054665441}$$

Iddividi \frac{1+\sqrt{12813994352897}}{50054665441} b'-2.

$$x=\frac{-\sqrt{12813994352897}-1}{100109330882}$$

Issa solvi l-ekwazzjoni x=\frac{\frac{1}{50054665441}±\frac{\sqrt{12813994352897}}{50054665441}}{-2} fejn ± hija minus. Naqqas \frac{\sqrt{12813994352897}}{50054665441} minn \frac{1}{50054665441}.

$$x=\frac{1-\sqrt{12813994352897}}{-2\times 50054665441}$$

Iddividi \frac{1-\sqrt{12813994352897}}{50054665441} b'-2.

$$x=\frac{\sqrt{12813994352897}-1}{100109330882}$$

L-ekwazzjoni issa solvuta.

$$x=\frac{-\sqrt{12813994352897}-1}{100109330882} x=\frac{\sqrt{12813994352897}-1}{100109330882}$$

Passi biex Tikkompleta l-Kwadrat

Il-varjabbli x ma jistax ikun ugwali għal 64 billi d-diviżjoni b'żero mhux iddefinit. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'-x+64.

$$\left(-x+64\right)\times 473^{-4}=x^{2}$$

Ikkalkula 473 bil-power ta' -4 u tikseb \frac{1}{50054665441}.

$$\left(-x+64\right)\times \frac{1}{50054665441}=x^{2}$$

Uża l-propjetà distributtiva biex timmultiplika -x+64 b'\frac{1}{50054665441}.

$$-\frac{1}{50054665441}x+\frac{64}{50054665441}=x^{2}$$

Naqqas x^{2} miż-żewġ naħat.

$$-\frac{1}{50054665441}x+\frac{64}{50054665441}-x^{2}=0$$

Naqqas \frac{64}{50054665441} miż-żewġ naħat. Xi ħaġa mnaqqsa minn żero tagħti numru negattiv.

$$-\frac{1}{50054665441}x-x^{2}=-\frac{64}{50054665441}$$

Ekwazzjonijiet kwadratiċi bħal din jistgħu jiġu solvuti billi tikkompleta l-kwadrat. Sabiex tikkompleta l-kwadrat, l-ekwazzjoni l-ewwel trid tkun fil-forma x^{2}+bx=c.

$$-x^{2}-\frac{1}{50054665441}x=-\frac{64}{50054665441}$$

Iddividi ż-żewġ naħat b'-1.

$$\frac{-x^{2}-\frac{1}{50054665441}x}{-1}=-\frac{\frac{64}{50054665441}}{-1}$$

Meta tiddividi b'-1 titneħħa l-multiplikazzjoni b'-1.

$$x^{2}+\left(-\frac{\frac{1}{50054665441}}{-1}\right)x=-\frac{\frac{64}{50054665441}}{-1}$$

Iddividi -\frac{1}{50054665441} b'-1.

$$x^{2}+\frac{1}{50054665441}x=-\frac{\frac{64}{50054665441}}{-1}$$

Iddividi -\frac{64}{50054665441} b'-1.

$$x^{2}+\frac{1}{50054665441}x=\frac{64}{50054665441}$$

Iddividi \frac{1}{50054665441}, il-koeffiċjent tat-terminu x, b'2 biex tikseb \frac{1}{100109330882}. Imbagħad żid il-kwadru ta' \frac{1}{100109330882} maż-żewġ naħat tal-ekwazzjoni. Dan il-pass jagħmel in-naħa tax-xellug tal-ekwazzjoni kwadru perfett.

$$x^{2}+\frac{1}{50054665441}x+\left(\frac{1}{100109330882}\right)^{2}=\frac{64}{50054665441}+\left(\frac{1}{100109330882}\right)^{2}$$

Ikkwadra \frac{1}{100109330882} billi tikkwadra kemm in-numeratur u d-denominatur tal-frazzjoni.

$$x^{2}+\frac{1}{50054665441}x+\frac{1}{10021878129641758897924}=\frac{64}{50054665441}+\frac{1}{10021878129641758897924}$$

Żid \frac{64}{50054665441} ma' \frac{1}{10021878129641758897924} biex issib id-denominatur komuni u żżid in-numeraturi. Imbagħad naqqas il-frazzjoni għat-termini l-aktar baxxi jekk possibbli.

$$x^{2}+\frac{1}{50054665441}x+\frac{1}{10021878129641758897924}=\frac{12813994352897}{10021878129641758897924}$$

Fattur x^{2}+\frac{1}{50054665441}x+\frac{1}{10021878129641758897924}. B'mod ġenerali, meta x^{2}+bx+c huwa kwadru perfett, dejjem jista' jiġu fatturati bħala \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{1}{100109330882}\right)^{2}=\frac{12813994352897}{10021878129641758897924}$$

Ħu l-għerq kwadrat taż-żewġ naħat tal-ekwazzjoni.

$$\sqrt{\left(x+\frac{1}{100109330882}\right)^{2}}=\sqrt{\frac{12813994352897}{10021878129641758897924}}$$

Issimplifika.

$$x+\frac{1}{100109330882}=\frac{\sqrt{12813994352897}}{100109330882} x+\frac{1}{100109330882}=-\frac{\sqrt{12813994352897}}{100109330882}$$

Naqqas \frac{1}{100109330882} miż-żewġ naħat tal-ekwazzjoni.

$$x=\frac{\sqrt{12813994352897}-1}{100109330882} x=\frac{-\sqrt{12813994352897}-1}{100109330882}$$