Issolvi 29/10=1/2{left(x-6/5right)}^2+32/25

$$\frac{ 29 }{ 10 } = \frac{ 1 }{ 2 } { \left(x- \frac{ 6 }{ 5 } \right) }^{ 2 } + \frac{ 32 }{ 25 }$$

Solvi għal x

$$x=3$$

$$x=-\frac{3}{5}=-0.6$$

Passi għall-Użu tal-Formula Kwadratika

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(x-\frac{6}{5}\right)^{2}.

$$\frac{29}{10}=\frac{1}{2}\left(x^{2}-\frac{12}{5}x+\frac{36}{25}\right)+\frac{32}{25}$$

Uża l-propjetà distributtiva biex timmultiplika \frac{1}{2} b'x^{2}-\frac{12}{5}x+\frac{36}{25}.

$$\frac{29}{10}=\frac{1}{2}x^{2}-\frac{6}{5}x+\frac{18}{25}+\frac{32}{25}$$

Żid \frac{18}{25} u \frac{32}{25} biex tikseb 2.

$$\frac{29}{10}=\frac{1}{2}x^{2}-\frac{6}{5}x+2$$

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$\frac{1}{2}x^{2}-\frac{6}{5}x+2=\frac{29}{10}$$

Naqqas \frac{29}{10} miż-żewġ naħat.

$$\frac{1}{2}x^{2}-\frac{6}{5}x+2-\frac{29}{10}=0$$

Naqqas \frac{29}{10} minn 2 biex tikseb -\frac{9}{10}.

$$\frac{1}{2}x^{2}-\frac{6}{5}x-\frac{9}{10}=0$$

Din l-ekwazzjoni hija fil-forma standard: ax^{2}+bx+c=0. Issostitwixxi \frac{1}{2} għal a, -\frac{6}{5} għal b, u -\frac{9}{10} għal c fil-formula kwadratika, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{6}{5}\right)±\sqrt{\left(-\frac{6}{5}\right)^{2}-4\times \frac{1}{2}\left(-\frac{9}{10}\right)}}{2\times \frac{1}{2}}$$

Ikkwadra -\frac{6}{5} billi tikkwadra kemm in-numeratur u d-denominatur tal-frazzjoni.

$$x=\frac{-\left(-\frac{6}{5}\right)±\sqrt{\frac{36}{25}-4\times \frac{1}{2}\left(-\frac{9}{10}\right)}}{2\times \frac{1}{2}}$$

Immultiplika -4 b'\frac{1}{2}.

$$x=\frac{-\left(-\frac{6}{5}\right)±\sqrt{\frac{36}{25}-2\left(-\frac{9}{10}\right)}}{2\times \frac{1}{2}}$$

Immultiplika -2 b'-\frac{9}{10}.

$$x=\frac{-\left(-\frac{6}{5}\right)±\sqrt{\frac{36}{25}+\frac{9}{5}}}{2\times \frac{1}{2}}$$

Żid \frac{36}{25} ma' \frac{9}{5} biex issib id-denominatur komuni u żżid in-numeraturi. Imbagħad naqqas il-frazzjoni għat-termini l-aktar baxxi jekk possibbli.

$$x=\frac{-\left(-\frac{6}{5}\right)±\sqrt{\frac{81}{25}}}{2\times \frac{1}{2}}$$

Ħu l-għerq kwadrat ta' \frac{81}{25}.

$$x=\frac{-\left(-\frac{6}{5}\right)±\frac{9}{5}}{2\times \frac{1}{2}}$$

L-oppost ta' -\frac{6}{5} huwa \frac{6}{5}.

$$x=\frac{\frac{6}{5}±\frac{9}{5}}{2\times \frac{1}{2}}$$

Immultiplika 2 b'\frac{1}{2}.

$$x=\frac{\frac{6}{5}±\frac{9}{5}}{1}$$

Issa solvi l-ekwazzjoni x=\frac{\frac{6}{5}±\frac{9}{5}}{1} fejn ± hija plus. Żid \frac{6}{5} ma' \frac{9}{5} biex issib id-denominatur komuni u żżid in-numeraturi. Imbagħad naqqas il-frazzjoni għat-termini l-aktar baxxi jekk possibbli.

$$x=\frac{3}{1}$$

Iddividi 3 b'1.

$$x=3$$

Issa solvi l-ekwazzjoni x=\frac{\frac{6}{5}±\frac{9}{5}}{1} fejn ± hija minus. Naqqas \frac{9}{5} minn \frac{6}{5} billi ssib denominatur komuni u tnaqqas in-numerators. Imbagħad naqqas il-frazzjoni għall-inqas termini jekk possibbli.

$$x=-\frac{\frac{3}{5}}{1}$$

Iddividi -\frac{3}{5} b'1.

$$x=-\frac{3}{5}$$

L-ekwazzjoni issa solvuta.

$$x=3 x=-\frac{3}{5}$$

Passi biex Tikkompleta l-Kwadrat

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(x-\frac{6}{5}\right)^{2}.

$$\frac{29}{10}=\frac{1}{2}\left(x^{2}-\frac{12}{5}x+\frac{36}{25}\right)+\frac{32}{25}$$

Uża l-propjetà distributtiva biex timmultiplika \frac{1}{2} b'x^{2}-\frac{12}{5}x+\frac{36}{25}.

$$\frac{29}{10}=\frac{1}{2}x^{2}-\frac{6}{5}x+\frac{18}{25}+\frac{32}{25}$$

Żid \frac{18}{25} u \frac{32}{25} biex tikseb 2.

$$\frac{29}{10}=\frac{1}{2}x^{2}-\frac{6}{5}x+2$$

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$\frac{1}{2}x^{2}-\frac{6}{5}x+2=\frac{29}{10}$$

Naqqas 2 miż-żewġ naħat.

$$\frac{1}{2}x^{2}-\frac{6}{5}x=\frac{29}{10}-2$$

Naqqas 2 minn \frac{29}{10} biex tikseb \frac{9}{10}.

$$\frac{1}{2}x^{2}-\frac{6}{5}x=\frac{9}{10}$$

Immultiplika ż-żewġ naħat b'2.

$$\frac{\frac{1}{2}x^{2}-\frac{6}{5}x}{\frac{1}{2}}=\frac{\frac{9}{10}}{\frac{1}{2}}$$

Meta tiddividi b'\frac{1}{2} titneħħa l-multiplikazzjoni b'\frac{1}{2}.

$$x^{2}+\left(-\frac{\frac{6}{5}}{\frac{1}{2}}\right)x=\frac{\frac{9}{10}}{\frac{1}{2}}$$

Iddividi -\frac{6}{5} b'\frac{1}{2} billi timmultiplika -\frac{6}{5} bir-reċiproku ta' \frac{1}{2}.

$$x^{2}-\frac{12}{5}x=\frac{\frac{9}{10}}{\frac{1}{2}}$$

Iddividi \frac{9}{10} b'\frac{1}{2} billi timmultiplika \frac{9}{10} bir-reċiproku ta' \frac{1}{2}.

$$x^{2}-\frac{12}{5}x=\frac{9}{5}$$

Iddividi -\frac{12}{5}, il-koeffiċjent tat-terminu x, b'2 biex tikseb -\frac{6}{5}. Imbagħad żid il-kwadru ta' -\frac{6}{5} maż-żewġ naħat tal-ekwazzjoni. Dan il-pass jagħmel in-naħa tax-xellug tal-ekwazzjoni kwadru perfett.

$$x^{2}-\frac{12}{5}x+\left(-\frac{6}{5}\right)^{2}=\frac{9}{5}+\left(-\frac{6}{5}\right)^{2}$$

Ikkwadra -\frac{6}{5} billi tikkwadra kemm in-numeratur u d-denominatur tal-frazzjoni.

$$x^{2}-\frac{12}{5}x+\frac{36}{25}=\frac{9}{5}+\frac{36}{25}$$

Żid \frac{9}{5} ma' \frac{36}{25} biex issib id-denominatur komuni u żżid in-numeraturi. Imbagħad naqqas il-frazzjoni għat-termini l-aktar baxxi jekk possibbli.

$$x^{2}-\frac{12}{5}x+\frac{36}{25}=\frac{81}{25}$$

Fattur x^{2}-\frac{12}{5}x+\frac{36}{25}. B'mod ġenerali, meta x^{2}+bx+c huwa kwadru perfett, dejjem jista' jiġu fatturati bħala \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{6}{5}\right)^{2}=\frac{81}{25}$$

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

$$\sqrt{\left(x-\frac{6}{5}\right)^{2}}=\sqrt{\frac{81}{25}}$$

Issimplifika.

$$x-\frac{6}{5}=\frac{9}{5} x-\frac{6}{5}=-\frac{9}{5}$$

Żid \frac{6}{5} maż-żewġ naħat tal-ekwazzjoni.

$$x=3 x=-\frac{3}{5}$$