Datrys x^2(6%)^2+(1-x)^2(2%)^2+2x(1-x)*012*6%*2%=00327

$$x ^ { 2 } ( 6 \% ) ^ { 2 } + ( 1 - x ) ^ { 2 } ( 2 \% ) ^ { 2 } + 2 x ( 1 - x ) \times 012 \times 6 \% \times 2 \% = 00327$$

Datrys ar gyfer x (complex solution)

$$x=\frac{1}{10}+\frac{3}{10}i=0.1+0.3i$$

$$x=\frac{1}{10}-\frac{3}{10}i=0.1-0.3i$$

Camau gan Ddefnyddio’r Fformiwla Cwadratig

Lleihau'r ffracsiwn \frac{6}{100} i'r graddau lleiaf posib drwy dynnu a chanslo allan 2.

$$x^{2}\times \left(\frac{3}{50}\right)^{2}+\left(1-x\right)^{2}\times \left(\frac{2}{100}\right)^{2}+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Cyfrifo \frac{3}{50} i bŵer 2 a chael \frac{9}{2500}.

$$x^{2}\times \frac{9}{2500}+\left(1-x\right)^{2}\times \left(\frac{2}{100}\right)^{2}+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(1-x\right)^{2}.

$$x^{2}\times \frac{9}{2500}+\left(1-2x+x^{2}\right)\times \left(\frac{2}{100}\right)^{2}+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Lleihau'r ffracsiwn \frac{2}{100} i'r graddau lleiaf posib drwy dynnu a chanslo allan 2.

$$x^{2}\times \frac{9}{2500}+\left(1-2x+x^{2}\right)\times \left(\frac{1}{50}\right)^{2}+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Cyfrifo \frac{1}{50} i bŵer 2 a chael \frac{1}{2500}.

$$x^{2}\times \frac{9}{2500}+\left(1-2x+x^{2}\right)\times \frac{1}{2500}+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Defnyddio’r briodwedd ddosbarthu i luosi 1-2x+x^{2} â \frac{1}{2500}.

$$x^{2}\times \frac{9}{2500}+\frac{1}{2500}-\frac{1}{1250}x+\frac{1}{2500}x^{2}+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Cyfuno x^{2}\times \frac{9}{2500} a \frac{1}{2500}x^{2} i gael \frac{1}{250}x^{2}.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Lluosi 2 a 0 i gael 0.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0x\left(1-x\right)\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Lluosi 0 a 12 i gael 0.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0x\left(1-x\right)\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Lleihau'r ffracsiwn \frac{6}{100} i'r graddau lleiaf posib drwy dynnu a chanslo allan 2.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0x\left(1-x\right)\times \frac{3}{50}\times \frac{2}{100}=0\times 0\times 327$$

Lluosi 0 a \frac{3}{50} i gael 0.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0x\left(1-x\right)\times \frac{2}{100}=0\times 0\times 327$$

Lleihau'r ffracsiwn \frac{2}{100} i'r graddau lleiaf posib drwy dynnu a chanslo allan 2.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0x\left(1-x\right)\times \frac{1}{50}=0\times 0\times 327$$

Lluosi 0 a \frac{1}{50} i gael 0.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0x\left(1-x\right)=0\times 0\times 327$$

Mae lluosi unrhyw beth â sero yn rhoi sero.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0=0\times 0\times 327$$

Adio \frac{1}{2500} a 0 i gael \frac{1}{2500}.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x=0\times 0\times 327$$

Lluosi 0 a 0 i gael 0.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x=0\times 327$$

Lluosi 0 a 327 i gael 0.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x=0$$

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.

$$\frac{1}{250}x^{2}-\frac{1}{1250}x+\frac{1}{2500}=0$$

Mae’r hafaliad hwn yn y ffurf safonol: ax^{2}+bx+c=0. Amnewidiwch \frac{1}{250} am a, -\frac{1}{1250} am b, a \frac{1}{2500} am c yn y fformiwla gwadratig, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{1}{1250}\right)±\sqrt{\left(-\frac{1}{1250}\right)^{2}-4\times \frac{1}{250}\times \frac{1}{2500}}}{2\times \frac{1}{250}}$$

Sgwariwch -\frac{1}{1250} drwy sgwario'r rhifiadur ag enwadur y ffracsiwn.

$$x=\frac{-\left(-\frac{1}{1250}\right)±\sqrt{\frac{1}{1562500}-4\times \frac{1}{250}\times \frac{1}{2500}}}{2\times \frac{1}{250}}$$

Lluoswch -4 â \frac{1}{250}.

$$x=\frac{-\left(-\frac{1}{1250}\right)±\sqrt{\frac{1}{1562500}-\frac{2}{125}\times \frac{1}{2500}}}{2\times \frac{1}{250}}$$

Lluoswch -\frac{2}{125} â \frac{1}{2500} drwy luosi'r rhifiadur â’r rhifiadur a'r enwadur â’r enwadur. Yna, dylech leihau’r ffracsiwn i’r termau isaf os yn bosibl.

$$x=\frac{-\left(-\frac{1}{1250}\right)±\sqrt{\frac{1}{1562500}-\frac{1}{156250}}}{2\times \frac{1}{250}}$$

Adio \frac{1}{1562500} at -\frac{1}{156250} drwy ddod o hyd i enwadur cyffredin ac ychwanegu’r rhifiaduron. Yna, lleihau’r ffracsiwn i’r termau isaf os yn bosibl.

$$x=\frac{-\left(-\frac{1}{1250}\right)±\sqrt{-\frac{9}{1562500}}}{2\times \frac{1}{250}}$$

Cymryd isradd -\frac{9}{1562500}.

$$x=\frac{-\left(-\frac{1}{1250}\right)±\frac{3}{1250}i}{2\times \frac{1}{250}}$$

Gwrthwyneb -\frac{1}{1250} yw \frac{1}{1250}.

$$x=\frac{\frac{1}{1250}±\frac{3}{1250}i}{2\times \frac{1}{250}}$$

Lluoswch 2 â \frac{1}{250}.

$$x=\frac{\frac{1}{1250}±\frac{3}{1250}i}{\frac{1}{125}}$$

Datryswch yr hafaliad x=\frac{\frac{1}{1250}±\frac{3}{1250}i}{\frac{1}{125}} pan fydd ± yn plws. Adio \frac{1}{1250} at \frac{3}{1250}i.

$$x=\frac{\frac{1}{1250}+\frac{3}{1250}i}{\frac{1}{125}}$$

Rhannwch \frac{1}{1250}+\frac{3}{1250}i â \frac{1}{125} drwy luosi \frac{1}{1250}+\frac{3}{1250}i â chilydd \frac{1}{125}.

$$x=\frac{1}{10}+\frac{3}{10}i$$

Datryswch yr hafaliad x=\frac{\frac{1}{1250}±\frac{3}{1250}i}{\frac{1}{125}} pan fydd ± yn minws. Tynnu \frac{3}{1250}i o \frac{1}{1250}.

$$x=\frac{\frac{1}{1250}-\frac{3}{1250}i}{\frac{1}{125}}$$

Rhannwch \frac{1}{1250}-\frac{3}{1250}i â \frac{1}{125} drwy luosi \frac{1}{1250}-\frac{3}{1250}i â chilydd \frac{1}{125}.

$$x=\frac{1}{10}-\frac{3}{10}i$$

Mae’r hafaliad wedi’i ddatrys nawr.

$$x=\frac{1}{10}+\frac{3}{10}i x=\frac{1}{10}-\frac{3}{10}i$$

Camau ar Gyfer Cwblhau'r Sgwâr

Lleihau'r ffracsiwn \frac{6}{100} i'r graddau lleiaf posib drwy dynnu a chanslo allan 2.

$$x^{2}\times \left(\frac{3}{50}\right)^{2}+\left(1-x\right)^{2}\times \left(\frac{2}{100}\right)^{2}+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Cyfrifo \frac{3}{50} i bŵer 2 a chael \frac{9}{2500}.

$$x^{2}\times \frac{9}{2500}+\left(1-x\right)^{2}\times \left(\frac{2}{100}\right)^{2}+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(1-x\right)^{2}.

$$x^{2}\times \frac{9}{2500}+\left(1-2x+x^{2}\right)\times \left(\frac{2}{100}\right)^{2}+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Lleihau'r ffracsiwn \frac{2}{100} i'r graddau lleiaf posib drwy dynnu a chanslo allan 2.

$$x^{2}\times \frac{9}{2500}+\left(1-2x+x^{2}\right)\times \left(\frac{1}{50}\right)^{2}+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Cyfrifo \frac{1}{50} i bŵer 2 a chael \frac{1}{2500}.

$$x^{2}\times \frac{9}{2500}+\left(1-2x+x^{2}\right)\times \frac{1}{2500}+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Defnyddio’r briodwedd ddosbarthu i luosi 1-2x+x^{2} â \frac{1}{2500}.

$$x^{2}\times \frac{9}{2500}+\frac{1}{2500}-\frac{1}{1250}x+\frac{1}{2500}x^{2}+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Cyfuno x^{2}\times \frac{9}{2500} a \frac{1}{2500}x^{2} i gael \frac{1}{250}x^{2}.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Lluosi 2 a 0 i gael 0.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0x\left(1-x\right)\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Lluosi 0 a 12 i gael 0.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0x\left(1-x\right)\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Lleihau'r ffracsiwn \frac{6}{100} i'r graddau lleiaf posib drwy dynnu a chanslo allan 2.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0x\left(1-x\right)\times \frac{3}{50}\times \frac{2}{100}=0\times 0\times 327$$

Lluosi 0 a \frac{3}{50} i gael 0.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0x\left(1-x\right)\times \frac{2}{100}=0\times 0\times 327$$

Lleihau'r ffracsiwn \frac{2}{100} i'r graddau lleiaf posib drwy dynnu a chanslo allan 2.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0x\left(1-x\right)\times \frac{1}{50}=0\times 0\times 327$$

Lluosi 0 a \frac{1}{50} i gael 0.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0x\left(1-x\right)=0\times 0\times 327$$

Mae lluosi unrhyw beth â sero yn rhoi sero.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0=0\times 0\times 327$$

Adio \frac{1}{2500} a 0 i gael \frac{1}{2500}.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x=0\times 0\times 327$$

Lluosi 0 a 0 i gael 0.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x=0\times 327$$

Lluosi 0 a 327 i gael 0.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x=0$$

Tynnu \frac{1}{2500} o'r ddwy ochr. Mae tynnu unrhyw beth o sero’n rhoi negydd y swm.

$$\frac{1}{250}x^{2}-\frac{1}{1250}x=-\frac{1}{2500}$$

Lluosi’r ddwy ochr â 250.

$$\frac{\frac{1}{250}x^{2}-\frac{1}{1250}x}{\frac{1}{250}}=-\frac{\frac{1}{2500}}{\frac{1}{250}}$$

Mae rhannu â \frac{1}{250} yn dad-wneud lluosi â \frac{1}{250}.

$$x^{2}+\left(-\frac{\frac{1}{1250}}{\frac{1}{250}}\right)x=-\frac{\frac{1}{2500}}{\frac{1}{250}}$$

Rhannwch -\frac{1}{1250} â \frac{1}{250} drwy luosi -\frac{1}{1250} â chilydd \frac{1}{250}.

$$x^{2}-\frac{1}{5}x=-\frac{\frac{1}{2500}}{\frac{1}{250}}$$

Rhannwch -\frac{1}{2500} â \frac{1}{250} drwy luosi -\frac{1}{2500} â chilydd \frac{1}{250}.

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

Rhannwch -\frac{1}{5}, cyfernod y term x, â 2 i gael -\frac{1}{10}. Yna ychwanegwch sgwâr -\frac{1}{10} at ddwy ochr yr hafaliad. Mae'r cam hwn yn gwneud ochr chwith yr hafaliad yn sgwâr perffaith.

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

Sgwariwch -\frac{1}{10} drwy sgwario'r rhifiadur ag enwadur y ffracsiwn.

$$x^{2}-\frac{1}{5}x+\frac{1}{100}=-\frac{1}{10}+\frac{1}{100}$$

Adio -\frac{1}{10} at \frac{1}{100} drwy ddod o hyd i enwadur cyffredin ac ychwanegu’r rhifiaduron. Yna, lleihau’r ffracsiwn i’r termau isaf os yn bosibl.

$$x^{2}-\frac{1}{5}x+\frac{1}{100}=-\frac{9}{100}$$

Ffactora x^{2}-\frac{1}{5}x+\frac{1}{100}. 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}.

$$\left(x-\frac{1}{10}\right)^{2}=-\frac{9}{100}$$

Cymrwch isradd dwy ochr yr hafaliad.

$$\sqrt{\left(x-\frac{1}{10}\right)^{2}}=\sqrt{-\frac{9}{100}}$$

Symleiddio.

$$x-\frac{1}{10}=\frac{3}{10}i x-\frac{1}{10}=-\frac{3}{10}i$$

Adio \frac{1}{10} at ddwy ochr yr hafaliad.

$$x=\frac{1}{10}+\frac{3}{10}i x=\frac{1}{10}-\frac{3}{10}i$$