Issolvi 1212^2=108^2+x^2-2*108*x*cos122^circ

$$1212 ^ { 2 } = 108 ^ { 2 } + x ^ { 2 } - 2 \cdot 108 \cdot x \cdot \cos 122 ^ { \circ }$$

Solvi għal x

$$x = \frac{3 \sqrt{3962010143966813418503407198897729} - 8942387583935331}{156250000000000} = 1151\frac{47363934469280}{156250000000000} \approx 1151.303129181$$

$$x=\frac{-3\sqrt{3962010143966813418503407198897729}-8942387583935331}{156250000000000}\approx -1265.765690255$$

Passi għall-Użu tal-Formula Kwadratika

Evaluate trigonometric functions in the problem

$$1212 ^ {2} = 108 ^ {2} + x ^ {2} - 2 \cdot 108 \cdot x \cdot -0.5299192642332048$$

Ikkalkula 1212 bil-power ta' 2 u tikseb 1468944.

$$1468944=108^{2}+x^{2}-2\times 108x\left(-0.5299192642332048\right)$$

Ikkalkula 108 bil-power ta' 2 u tikseb 11664.

$$1468944=11664+x^{2}-2\times 108x\left(-0.5299192642332048\right)$$

Immultiplika 2 u 108 biex tikseb 216.

$$1468944=11664+x^{2}-216x\left(-0.5299192642332048\right)$$

Immultiplika 216 u -0.5299192642332048 biex tikseb -114.4625610743722368.

$$1468944=11664+x^{2}-\left(-114.4625610743722368x\right)$$

L-oppost ta' -114.4625610743722368x huwa 114.4625610743722368x.

$$1468944=11664+x^{2}+114.4625610743722368x$$

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

$$11664+x^{2}+114.4625610743722368x=1468944$$

Naqqas 1468944 miż-żewġ naħat.

$$11664+x^{2}+114.4625610743722368x-1468944=0$$

Naqqas 1468944 minn 11664 biex tikseb -1457280.

$$-1457280+x^{2}+114.4625610743722368x=0$$

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.

$$x^{2}+114.4625610743722368x-1457280=0$$

Din l-ekwazzjoni hija fil-forma standard: ax^{2}+bx+c=0. Issostitwixxi 1 għal a, 114.4625610743722368 għal b, u -1457280 għal c fil-formula kwadratika, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-114.4625610743722368±\sqrt{114.4625610743722368^{2}-4\left(-1457280\right)}}{2}$$

Ikkwadra 114.4625610743722368 billi tikkwadra kemm in-numeratur u d-denominatur tal-frazzjoni.

$$x=\frac{-114.4625610743722368±\sqrt{13101.67788770439438838411920663527424-4\left(-1457280\right)}}{2}$$

Immultiplika -4 b'-1457280.

$$x=\frac{-114.4625610743722368±\sqrt{13101.67788770439438838411920663527424+5829120}}{2}$$

Żid 13101.67788770439438838411920663527424 ma' 5829120.

$$x=\frac{-114.4625610743722368±\sqrt{5842221.67788770439438838411920663527424}}{2}$$

Ħu l-għerq kwadrat ta' 5842221.67788770439438838411920663527424.

$$x=\frac{-114.4625610743722368±\frac{3\sqrt{3962010143966813418503407198897729}}{78125000000000}}{2}$$

Issa solvi l-ekwazzjoni x=\frac{-114.4625610743722368±\frac{3\sqrt{3962010143966813418503407198897729}}{78125000000000}}{2} fejn ± hija plus. Żid -114.4625610743722368 ma' \frac{3\sqrt{3962010143966813418503407198897729}}{78125000000000}.

$$x=\frac{3\sqrt{3962010143966813418503407198897729}-8942387583935331}{2\times 78125000000000}$$

Iddividi \frac{-8942387583935331+3\sqrt{3962010143966813418503407198897729}}{78125000000000} b'2.

$$x=\frac{3\sqrt{3962010143966813418503407198897729}-8942387583935331}{156250000000000}$$

Issa solvi l-ekwazzjoni x=\frac{-114.4625610743722368±\frac{3\sqrt{3962010143966813418503407198897729}}{78125000000000}}{2} fejn ± hija minus. Naqqas \frac{3\sqrt{3962010143966813418503407198897729}}{78125000000000} minn -114.4625610743722368.

$$x=\frac{-3\sqrt{3962010143966813418503407198897729}-8942387583935331}{2\times 78125000000000}$$

Iddividi \frac{-8942387583935331-3\sqrt{3962010143966813418503407198897729}}{78125000000000} b'2.

$$x=\frac{-3\sqrt{3962010143966813418503407198897729}-8942387583935331}{156250000000000}$$

L-ekwazzjoni issa solvuta.

$$x=\frac{3\sqrt{3962010143966813418503407198897729}-8942387583935331}{156250000000000} x=\frac{-3\sqrt{3962010143966813418503407198897729}-8942387583935331}{156250000000000}$$

Passi biex Tikkompleta l-Kwadrat

Evaluate trigonometric functions in the problem

$$1212 ^ {2} = 108 ^ {2} + x ^ {2} - 2 \cdot 108 \cdot x \cdot -0.5299192642332048$$

Ikkalkula 1212 bil-power ta' 2 u tikseb 1468944.

$$1468944=108^{2}+x^{2}-2\times 108x\left(-0.5299192642332048\right)$$

Ikkalkula 108 bil-power ta' 2 u tikseb 11664.

$$1468944=11664+x^{2}-2\times 108x\left(-0.5299192642332048\right)$$

Immultiplika 2 u 108 biex tikseb 216.

$$1468944=11664+x^{2}-216x\left(-0.5299192642332048\right)$$

Immultiplika 216 u -0.5299192642332048 biex tikseb -114.4625610743722368.

$$1468944=11664+x^{2}-\left(-114.4625610743722368x\right)$$

L-oppost ta' -114.4625610743722368x huwa 114.4625610743722368x.

$$1468944=11664+x^{2}+114.4625610743722368x$$

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

$$11664+x^{2}+114.4625610743722368x=1468944$$

Naqqas 11664 miż-żewġ naħat.

$$x^{2}+114.4625610743722368x=1468944-11664$$

Naqqas 11664 minn 1468944 biex tikseb 1457280.

$$x^{2}+114.4625610743722368x=1457280$$

Iddividi 114.4625610743722368, il-koeffiċjent tat-terminu x, b'2 biex tikseb 57.2312805371861184. Imbagħad żid il-kwadru ta' 57.2312805371861184 maż-żewġ naħat tal-ekwazzjoni. Dan il-pass jagħmel in-naħa tax-xellug tal-ekwazzjoni kwadru perfett.

$$x^{2}+114.4625610743722368x+57.2312805371861184^{2}=1457280+57.2312805371861184^{2}$$

Ikkwadra 57.2312805371861184 billi tikkwadra kemm in-numeratur u d-denominatur tal-frazzjoni.

$$x^{2}+114.4625610743722368x+3275.41947192609859709602980165881856=1457280+3275.41947192609859709602980165881856$$

Żid 1457280 ma' 3275.41947192609859709602980165881856.

$$x^{2}+114.4625610743722368x+3275.41947192609859709602980165881856=1460555.41947192609859709602980165881856$$

Fattur x^{2}+114.4625610743722368x+3275.41947192609859709602980165881856. B'mod ġenerali, meta x^{2}+bx+c huwa kwadru perfett, dejjem jista' jiġu fatturati bħala \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+57.2312805371861184\right)^{2}=1460555.41947192609859709602980165881856$$

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

$$\sqrt{\left(x+57.2312805371861184\right)^{2}}=\sqrt{1460555.41947192609859709602980165881856}$$

Issimplifika.

$$x+57.2312805371861184=\frac{3\sqrt{3962010143966813418503407198897729}}{156250000000000} x+57.2312805371861184=-\frac{3\sqrt{3962010143966813418503407198897729}}{156250000000000}$$

Naqqas 57.2312805371861184 miż-żewġ naħat tal-ekwazzjoni.

$$x=\frac{3\sqrt{3962010143966813418503407198897729}-8942387583935331}{156250000000000} x=\frac{-3\sqrt{3962010143966813418503407198897729}-8942387583935331}{156250000000000}$$