Issolvi 50/17*9800+34*9800h=26500(h^2-8875^2)

$$\frac { 50 } { 17 } \times 9800 + 34 \times 9800 h = 26500 ( h ^ { 2 } - 8875 ^ { 2 } )$$

Solvi għal h

$$h=\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265}\approx 8881.289080421$$

$$h=-\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265}\approx -8868.715495515$$

Passi għall-Użu tal-Formula Kwadratika

Immultiplika \frac{50}{17} u 9800 biex tikseb \frac{490000}{17}.

$$\frac{490000}{17}+34\times 9800h=26500\left(h^{2}-8875^{2}\right)$$

Immultiplika 34 u 9800 biex tikseb 333200.

$$\frac{490000}{17}+333200h=26500\left(h^{2}-8875^{2}\right)$$

Ikkalkula 8875 bil-power ta' 2 u tikseb 78765625.

$$\frac{490000}{17}+333200h=26500\left(h^{2}-78765625\right)$$

Uża l-propjetà distributtiva biex timmultiplika 26500 b'h^{2}-78765625.

$$\frac{490000}{17}+333200h=26500h^{2}-2087289062500$$

Naqqas 26500h^{2} miż-żewġ naħat.

$$\frac{490000}{17}+333200h-26500h^{2}=-2087289062500$$

Żid 2087289062500 maż-żewġ naħat.

$$\frac{490000}{17}+333200h-26500h^{2}[phone]=0$$

Żid \frac{490000}{17} u 2087289062500 biex tikseb \frac{35483914552500}{17}.

$$\frac{35483914552500}{17}+333200h-26500h^{2}=0$$

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.

$$-26500h^{2}+333200h+\frac{35483914552500}{17}=0$$

Din l-ekwazzjoni hija fil-forma standard: ax^{2}+bx+c=0. Issostitwixxi -26500 għal a, 333200 għal b, u \frac{35483914552500}{17} għal c fil-formula kwadratika, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$h=\frac{-333200±\sqrt{333200^{2}-4\left(-26500\right)\times \frac{35483914552500}{17}}}{2\left(-26500\right)}$$

Ikkwadra 333200.

$$h=\frac{-333200±\sqrt{111022240000-4\left(-26500\right)\times \frac{35483914552500}{17}}}{2\left(-26500\right)}$$

Immultiplika -4 b'-26500.

$$h=\frac{-333200±\sqrt{111022240000+106000\times \frac{35483914552500}{17}}}{2\left(-26500\right)}$$

Immultiplika 106000 b'\frac{35483914552500}{17}.

$$h=\frac{-333200±\sqrt{111022240000+\frac{3761294942565000000}{17}}}{2\left(-26500\right)}$$

Żid 111022240000 ma' \frac{3761294942565000000}{17}.

$$h=\frac{-333200±\sqrt{\frac{3761296829943080000}{17}}}{2\left(-26500\right)}$$

Ħu l-għerq kwadrat ta' \frac{3761296829943080000}{17}.

$$h=\frac{-333200±\frac{200\sqrt{1598551152725809}}{17}}{2\left(-26500\right)}$$

Immultiplika 2 b'-26500.

$$h=\frac{-333200±\frac{200\sqrt{1598551152725809}}{17}}{-53000}$$

Issa solvi l-ekwazzjoni h=\frac{-333200±\frac{200\sqrt{1598551152725809}}{17}}{-53000} fejn ± hija plus. Żid -333200 ma' \frac{200\sqrt{1598551152725809}}{17}.

$$h=\frac{\frac{200\sqrt{1598551152725809}}{17}-333200}{-53000}$$

Iddividi -333200+\frac{200\sqrt{1598551152725809}}{17} b'-53000.

$$h=-\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265}$$

Issa solvi l-ekwazzjoni h=\frac{-333200±\frac{200\sqrt{1598551152725809}}{17}}{-53000} fejn ± hija minus. Naqqas \frac{200\sqrt{1598551152725809}}{17} minn -333200.

$$h=\frac{-\frac{200\sqrt{1598551152725809}}{17}-333200}{-53000}$$

Iddividi -333200-\frac{200\sqrt{1598551152725809}}{17} b'-53000.

$$h=\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265}$$

L-ekwazzjoni issa solvuta.

$$h=-\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265} h=\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265}$$

Passi biex Tikkompleta l-Kwadrat

Immultiplika \frac{50}{17} u 9800 biex tikseb \frac{490000}{17}.

$$\frac{490000}{17}+34\times 9800h=26500\left(h^{2}-8875^{2}\right)$$

Immultiplika 34 u 9800 biex tikseb 333200.

$$\frac{490000}{17}+333200h=26500\left(h^{2}-8875^{2}\right)$$

Ikkalkula 8875 bil-power ta' 2 u tikseb 78765625.

$$\frac{490000}{17}+333200h=26500\left(h^{2}-78765625\right)$$

Uża l-propjetà distributtiva biex timmultiplika 26500 b'h^{2}-78765625.

$$\frac{490000}{17}+333200h=26500h^{2}-2087289062500$$

Naqqas 26500h^{2} miż-żewġ naħat.

$$\frac{490000}{17}+333200h-26500h^{2}=-2087289062500$$

Naqqas \frac{490000}{17} miż-żewġ naħat.

$$333200h-26500h^{2}=-2087289062500-\frac{490000}{17}$$

Naqqas \frac{490000}{17} minn -2087289062500 biex tikseb -\frac{35483914552500}{17}.

$$333200h-26500h^{2}=-\frac{35483914552500}{17}$$

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.

$$-26500h^{2}+333200h=-\frac{35483914552500}{17}$$

Iddividi ż-żewġ naħat b'-26500.

$$\frac{-26500h^{2}+333200h}{-26500}=-\frac{\frac{35483914552500}{17}}{-26500}$$

Meta tiddividi b'-26500 titneħħa l-multiplikazzjoni b'-26500.

$$h^{2}+\frac{333200}{-26500}h=-\frac{\frac{35483914552500}{17}}{-26500}$$

Naqqas il-frazzjoni \frac{333200}{-26500} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 100.

$$h^{2}-\frac{3332}{265}h=-\frac{\frac{35483914552500}{17}}{-26500}$$

Iddividi -\frac{35483914552500}{17} b'-26500.

$$h^{2}-\frac{3332}{265}h=\frac{70967829105}{901}$$

Iddividi -\frac{3332}{265}, il-koeffiċjent tat-terminu x, b'2 biex tikseb -\frac{1666}{265}. Imbagħad żid il-kwadru ta' -\frac{1666}{265} maż-żewġ naħat tal-ekwazzjoni. Dan il-pass jagħmel in-naħa tax-xellug tal-ekwazzjoni kwadru perfett.

$$h^{2}-\frac{3332}{265}h+\left(-\frac{1666}{265}\right)^{2}=\frac{70967829105}{901}+\left(-\frac{1666}{265}\right)^{2}$$

Ikkwadra -\frac{1666}{265} billi tikkwadra kemm in-numeratur u d-denominatur tal-frazzjoni.

$$h^{2}-\frac{3332}{265}h+\frac{2775556}{70225}=\frac{70967829105}{901}+\frac{2775556}{70225}$$

Żid \frac{70967829105}{901} ma' \frac{2775556}{70225} biex issib id-denominatur komuni u żżid in-numeraturi. Imbagħad naqqas il-frazzjoni għat-termini l-aktar baxxi jekk possibbli.

$$h^{2}-\frac{3332}{265}h+\frac{2775556}{70225}=\frac{94032420748577}{1193825}$$

Fattur h^{2}-\frac{3332}{265}h+\frac{2775556}{70225}. B'mod ġenerali, meta x^{2}+bx+c huwa kwadru perfett, dejjem jista' jiġu fatturati bħala \left(x+\frac{b}{2}\right)^{2}.

$$\left(h-\frac{1666}{265}\right)^{2}=\frac{94032420748577}{1193825}$$

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

$$\sqrt{\left(h-\frac{1666}{265}\right)^{2}}=\sqrt{\frac{94032420748577}{1193825}}$$

Issimplifika.

$$h-\frac{1666}{265}=\frac{\sqrt{1598551152725809}}{4505} h-\frac{1666}{265}=-\frac{\sqrt{1598551152725809}}{4505}$$

Żid \frac{1666}{265} maż-żewġ naħat tal-ekwazzjoni.

$$h=\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265} h=-\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265}$$