Datrys sqrt{4578}x^2-sqrt{4677521}x+31478=10523

$$\sqrt{ 4578 } { x }^{ 2 } - \sqrt{ 4677521 } x+31478=10523$$

Datrys ar gyfer x (complex solution)

$$x=\frac{\sqrt{21413691138}+i\sqrt{383727960\sqrt{4578}-21413691138}}{9156}\approx 15.982325934+7.366910212i$$

$$x=\frac{-i\sqrt{383727960\sqrt{4578}-21413691138}+\sqrt{21413691138}}{9156}\approx 15.982325934-7.366910212i$$

Camau gan Ddefnyddio’r Fformiwla Cwadratig

Tynnu 10523 o'r ddwy ochr.

$$\sqrt{4578}x^{2}-\sqrt{4677521}x+31478-10523=0$$

Tynnu 10523 o 31478 i gael 20955.

$$\sqrt{4578}x^{2}-\sqrt{4677521}x+20955=0$$

Mae modd datrys pob hafaliad sydd yn y ffurf ax^{2}+bx+c=0 drwy ddefnyddio'r fformiwla cwadratig: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Mae'r fformiwla cwadratig yn rhoi dau ateb, pan fydd ± yn adio â’r llall pan fydd yn tynnu.

$$\sqrt{4578}x^{2}+\left(-\sqrt{4677521}\right)x+20955=0$$

Mae’r hafaliad hwn yn y ffurf safonol: ax^{2}+bx+c=0. Amnewidiwch \sqrt{4578} am a, -\sqrt{4677521} am b, a 20955 am c yn y fformiwla gwadratig, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\sqrt{4677521}\right)±\sqrt{\left(-\sqrt{4677521}\right)^{2}-4\sqrt{4578}\times 20955}}{2\sqrt{4578}}$$

Sgwâr -\sqrt{4677521}.

$$x=\frac{-\left(-\sqrt{4677521}\right)±\sqrt{4677521-4\sqrt{4578}\times 20955}}{2\sqrt{4578}}$$

Lluoswch -4 â \sqrt{4578}.

$$x=\frac{-\left(-\sqrt{4677521}\right)±\sqrt{4677521+\left(-4\sqrt{4578}\right)\times 20955}}{2\sqrt{4578}}$$

Lluoswch -4\sqrt{4578} â 20955.

$$x=\frac{-\left(-\sqrt{4677521}\right)±\sqrt{4677521-83820\sqrt{4578}}}{2\sqrt{4578}}$$

Cymryd isradd 4677521-83820\sqrt{4578}.

$$x=\frac{-\left(-\sqrt{4677521}\right)±i\sqrt{-\left(4677521-83820\sqrt{4578}\right)}}{2\sqrt{4578}}$$

Gwrthwyneb -\sqrt{4677521} yw \sqrt{4677521}.

$$x=\frac{\sqrt{4677521}±i\sqrt{-\left(4677521-83820\sqrt{4578}\right)}}{2\sqrt{4578}}$$

Datryswch yr hafaliad x=\frac{\sqrt{4677521}±i\sqrt{-\left(4677521-83820\sqrt{4578}\right)}}{2\sqrt{4578}} pan fydd ± yn plws. Adio \sqrt{4677521} at i\sqrt{-\left(4677521-83820\sqrt{4578}\right)}.

$$x=\frac{\sqrt{4677521}+i\sqrt{83820\sqrt{4578}-4677521}}{2\sqrt{4578}}$$

Rhannwch \sqrt{4677521}+i\sqrt{-4677521+83820\sqrt{4578}} â 2\sqrt{4578}.

$$x=\frac{\sqrt{4578}\left(\sqrt{4677521}+i\sqrt{83820\sqrt{4578}-4677521}\right)}{9156}$$

Datryswch yr hafaliad x=\frac{\sqrt{4677521}±i\sqrt{-\left(4677521-83820\sqrt{4578}\right)}}{2\sqrt{4578}} pan fydd ± yn minws. Tynnu i\sqrt{-\left(4677521-83820\sqrt{4578}\right)} o \sqrt{4677521}.

$$x=\frac{-i\sqrt{83820\sqrt{4578}-4677521}+\sqrt{4677521}}{2\sqrt{4578}}$$

Rhannwch \sqrt{4677521}-i\sqrt{-4677521+83820\sqrt{4578}} â 2\sqrt{4578}.

$$x=\frac{\sqrt{4578}\left(-i\sqrt{83820\sqrt{4578}-4677521}+\sqrt{4677521}\right)}{9156}$$

Mae’r hafaliad wedi’i ddatrys nawr.

$$x=\frac{\sqrt{4578}\left(\sqrt{4677521}+i\sqrt{83820\sqrt{4578}-4677521}\right)}{9156} x=\frac{\sqrt{4578}\left(-i\sqrt{83820\sqrt{4578}-4677521}+\sqrt{4677521}\right)}{9156}$$

Camau ar Gyfer Cwblhau'r Sgwâr

Tynnu 31478 o'r ddwy ochr.

$$\sqrt{4578}x^{2}-\sqrt{4677521}x=10523-31478$$

Tynnu 31478 o 10523 i gael -20955.

$$\sqrt{4578}x^{2}-\sqrt{4677521}x=-20955$$

Mae modd datrys hafaliadau cwadratig fel hwn drwy gwblhau’r sgwâr. Er mwyn cwblhau’r sgwâr, yn gyntaf mae’n rhaid i'r hafaliad fod ar ffurf x^{2}+bx=c.

$$\sqrt{4578}x^{2}+\left(-\sqrt{4677521}\right)x=-20955$$

Rhannu’r ddwy ochr â \sqrt{4578}.

$$\frac{\sqrt{4578}x^{2}+\left(-\sqrt{4677521}\right)x}{\sqrt{4578}}=-\frac{20955}{\sqrt{4578}}$$

Mae rhannu â \sqrt{4578} yn dad-wneud lluosi â \sqrt{4578}.

$$x^{2}+\left(-\frac{\sqrt{4677521}}{\sqrt{4578}}\right)x=-\frac{20955}{\sqrt{4578}}$$

Rhannwch -\sqrt{4677521} â \sqrt{4578}.

$$x^{2}+\left(-\frac{\sqrt{21413691138}}{4578}\right)x=-\frac{20955}{\sqrt{4578}}$$

Rhannwch -20955 â \sqrt{4578}.

$$x^{2}+\left(-\frac{\sqrt{21413691138}}{4578}\right)x=-\frac{6985\sqrt{4578}}{1526}$$

Rhannwch -\frac{\sqrt{21413691138}}{4578}, cyfernod y term x, â 2 i gael -\frac{\sqrt{21413691138}}{9156}. Yna ychwanegwch sgwâr -\frac{\sqrt{21413691138}}{9156} at ddwy ochr yr hafaliad. Mae'r cam hwn yn gwneud ochr chwith yr hafaliad yn sgwâr perffaith.

$$x^{2}+\left(-\frac{\sqrt{21413691138}}{4578}\right)x+\left(-\frac{\sqrt{21413691138}}{9156}\right)^{2}=-\frac{6985\sqrt{4578}}{1526}+\left(-\frac{\sqrt{21413691138}}{9156}\right)^{2}$$

Sgwâr -\frac{\sqrt{21413691138}}{9156}.

$$x^{2}+\left(-\frac{\sqrt{21413691138}}{4578}\right)x+\frac{4677521}{18312}=-\frac{6985\sqrt{4578}}{1526}+\frac{4677521}{18312}$$

Ffactora x^{2}+\left(-\frac{\sqrt{21413691138}}{4578}\right)x+\frac{4677521}{18312}. Yn gyffredinol, pan fydd x^{2}+bx+c yn sgwâr perffaith, mae modd ei ffactora bob amser fel \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{\sqrt{21413691138}}{9156}\right)^{2}=-\frac{6985\sqrt{4578}}{1526}+\frac{4677521}{18312}$$

Cymrwch isradd dwy ochr yr hafaliad.

$$\sqrt{\left(x-\frac{\sqrt{21413691138}}{9156}\right)^{2}}=\sqrt{-\frac{6985\sqrt{4578}}{1526}+\frac{4677521}{18312}}$$

Symleiddio.

$$x-\frac{\sqrt{21413691138}}{9156}=\frac{i\sqrt{383727960\sqrt{4578}-21413691138}}{9156} x-\frac{\sqrt{21413691138}}{9156}=-\frac{i\sqrt{383727960\sqrt{4578}-21413691138}}{9156}$$

Adio \frac{\sqrt{21413691138}}{9156} at ddwy ochr yr hafaliad.

$$x=\frac{\sqrt{21413691138}+i\sqrt{383727960\sqrt{4578}-21413691138}}{9156} x=\frac{-i\sqrt{383727960\sqrt{4578}-21413691138}+\sqrt{21413691138}}{9156}$$