Datrys x^2/(4-x)(1-x)=13*10^9

$$\frac { x ^ { 2 } } { ( 4 - x ) ( 1 - x ) } = 13 \times 10 ^ { 9 }$$

Datrys ar gyfer x

$$x = \frac{20000 \sqrt{950625000130} + 32500000000}{12999999999} \approx 4$$

$$x=\frac{32500000000-20000\sqrt{950625000130}}{12999999999}\approx 1$$

Camau gan Ddefnyddio’r Fformiwla Cwadratig

All y newidyn x ddim fod yn hafal i unrhyw un o’r gwerthoedd 1,4 gan nad ydy rhannu â sero wedi’i ddiffinio. Lluoswch ddwy ochr yr hafaliad â \left(x-4\right)\left(x-1\right).

$$x^{2}=13\times 10^{9}\left(x-4\right)\left(x-1\right)$$

Cyfrifo 10 i bŵer 9 a chael 1000000000.

$$x^{2}=13\times 1000000000\left(x-4\right)\left(x-1\right)$$

Lluosi 13 a 1000000000 i gael 13000000000.

$$x^{2}=13000000000\left(x-4\right)\left(x-1\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi 13000000000 â x-4.

$$x^{2}=\left(13000000000x-52000000000\right)\left(x-1\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi 13000000000x-52000000000 â x-1 a chyfuno termau tebyg.

$$x^{2}=13000000000x^{2}-65000000000x+52000000000$$

Tynnu 13000000000x^{2} o'r ddwy ochr.

$$x^{2}-13000000000x^{2}=-65000000000x+52000000000$$

Cyfuno x^{2} a -13000000000x^{2} i gael -12999999999x^{2}.

$$-12999999999x^{2}=-65000000000x+52000000000$$

Ychwanegu 65000000000x at y ddwy ochr.

$$-12999999999x^{2}[phone]x=52000000000$$

Tynnu 52000000000 o'r ddwy ochr.

$$-12999999999x^{2}[phone]x-52000000000=0$$

Mae’r hafaliad hwn yn y ffurf safonol: ax^{2}+bx+c=0. Amnewidiwch -12999999999 am a, 65000000000 am b, a -52000000000 am c yn y fformiwla gwadratig, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-65000000000±\sqrt{65000000000^{2}-4\left(-12999999999\right)\left(-52000000000\right)}}{2\left(-12999999999\right)}$$

Sgwâr 65000000000.

$$x=\frac{-65000000000±\sqrt{4225000000000000000000-4\left(-12999999999\right)\left(-52000000000\right)}}{2\left(-12999999999\right)}$$

Lluoswch -4 â -12999999999.

$$x=\frac{-65000000000±\sqrt{4225000000000000000000+51999999996\left(-52000000000\right)}}{2\left(-12999999999\right)}$$

Lluoswch 51999999996 â -52000000000.

$$x=\frac{-65000000000±\sqrt{4225000000000000000000-2703999999792000000000}}{2\left(-12999999999\right)}$$

Adio 4225000000000000000000 at -2703999999792000000000.

$$x=\frac{-65000000000±\sqrt{1521000000208000000000}}{2\left(-12999999999\right)}$$

Cymryd isradd 1521000000208000000000.

$$x=\frac{-65000000000±40000\sqrt{950625000130}}{2\left(-12999999999\right)}$$

Lluoswch 2 â -12999999999.

$$x=\frac{-65000000000±40000\sqrt{950625000130}}{-25999999998}$$

Datryswch yr hafaliad x=\frac{-65000000000±40000\sqrt{950625000130}}{-25999999998} pan fydd ± yn plws. Adio -65000000000 at 40000\sqrt{950625000130}.

$$x=\frac{40000\sqrt{950625000130}-65000000000}{-25999999998}$$

Rhannwch -65000000000+40000\sqrt{950625000130} â -25999999998.

$$x=\frac{32500000000-20000\sqrt{950625000130}}{12999999999}$$

Datryswch yr hafaliad x=\frac{-65000000000±40000\sqrt{950625000130}}{-25999999998} pan fydd ± yn minws. Tynnu 40000\sqrt{950625000130} o -65000000000.

$$x=\frac{-40000\sqrt{950625000130}-65000000000}{-25999999998}$$

Rhannwch -65000000000-40000\sqrt{950625000130} â -25999999998.

$$x=\frac{20000\sqrt{950625000130}[phone]}{12999999999}$$

Mae’r hafaliad wedi’i ddatrys nawr.

$$x=\frac{32500000000-20000\sqrt{950625000130}}{12999999999} x=\frac{20000\sqrt{950625000130}[phone]}{12999999999}$$

Camau ar Gyfer Cwblhau'r Sgwâr

All y newidyn x ddim fod yn hafal i unrhyw un o’r gwerthoedd 1,4 gan nad ydy rhannu â sero wedi’i ddiffinio. Lluoswch ddwy ochr yr hafaliad â \left(x-4\right)\left(x-1\right).

$$x^{2}=13\times 10^{9}\left(x-4\right)\left(x-1\right)$$

Cyfrifo 10 i bŵer 9 a chael 1000000000.

$$x^{2}=13\times 1000000000\left(x-4\right)\left(x-1\right)$$

Lluosi 13 a 1000000000 i gael 13000000000.

$$x^{2}=13000000000\left(x-4\right)\left(x-1\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi 13000000000 â x-4.

$$x^{2}=\left(13000000000x-52000000000\right)\left(x-1\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi 13000000000x-52000000000 â x-1 a chyfuno termau tebyg.

$$x^{2}=13000000000x^{2}-65000000000x+52000000000$$

Tynnu 13000000000x^{2} o'r ddwy ochr.

$$x^{2}-13000000000x^{2}=-65000000000x+52000000000$$

Cyfuno x^{2} a -13000000000x^{2} i gael -12999999999x^{2}.

$$-12999999999x^{2}=-65000000000x+52000000000$$

Ychwanegu 65000000000x at y ddwy ochr.

$$-12999999999x^{2}[phone]x=52000000000$$

Rhannu’r ddwy ochr â -12999999999.

$$\frac{-12999999999x^{2}[phone]x}{-12999999999}=\frac{52000000000}{-12999999999}$$

Mae rhannu â -12999999999 yn dad-wneud lluosi â -12999999999.

$$x^{2}+\frac{65000000000}{-12999999999}x=\frac{52000000000}{-12999999999}$$

Rhannwch 65000000000 â -12999999999.

$$x^{2}-\frac{65000000000}{12999999999}x=\frac{52000000000}{-12999999999}$$

Rhannwch 52000000000 â -12999999999.

$$x^{2}-\frac{65000000000}{12999999999}x=-\frac{52000000000}{12999999999}$$

Rhannwch -\frac{65000000000}{12999999999}, cyfernod y term x, â 2 i gael -\frac{32500000000}{12999999999}. Yna ychwanegwch sgwâr -\frac{32500000000}{12999999999} at ddwy ochr yr hafaliad. Mae'r cam hwn yn gwneud ochr chwith yr hafaliad yn sgwâr perffaith.

$$x^{2}-\frac{65000000000}{12999999999}x+\left(-\frac{32500000000}{12999999999}\right)^{2}=-\frac{52000000000}{12999999999}+\left(-\frac{32500000000}{12999999999}\right)^{2}$$

Sgwariwch -\frac{32500000000}{12999999999} drwy sgwario'r rhifiadur ag enwadur y ffracsiwn.

$$x^{2}-\frac{65000000000}{12999999999}x+\frac{1056250000000000000000}{168999999974000000001}=-\frac{52000000000}{12999999999}+\frac{1056250000000000000000}{168999999974000000001}$$

Adio -\frac{52000000000}{12999999999} at \frac{1056250000000000000000}{168999999974000000001} drwy ddod o hyd i enwadur cyffredin ac ychwanegu’r rhifiaduron. Yna, lleihau’r ffracsiwn i’r termau isaf os yn bosibl.

$$x^{2}-\frac{65000000000}{12999999999}x+\frac{1056250000000000000000}{168999999974000000001}=\frac{380250000052000000000}{168999999974000000001}$$

Ffactora x^{2}-\frac{65000000000}{12999999999}x+\frac{1056250000000000000000}{168999999974000000001}. 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}.

$$\left(x-\frac{32500000000}{12999999999}\right)^{2}=\frac{380250000052000000000}{168999999974000000001}$$

Cymrwch isradd dwy ochr yr hafaliad.

$$\sqrt{\left(x-\frac{32500000000}{12999999999}\right)^{2}}=\sqrt{\frac{380250000052000000000}{168999999974000000001}}$$

Symleiddio.

$$x-\frac{32500000000}{12999999999}=\frac{20000\sqrt{950625000130}}{12999999999} x-\frac{32500000000}{12999999999}=-\frac{20000\sqrt{950625000130}}{12999999999}$$

Adio \frac{32500000000}{12999999999} at ddwy ochr yr hafaliad.

$$x=\frac{20000\sqrt{950625000130}[phone]}{12999999999} x=\frac{32500000000-20000\sqrt{950625000130}}{12999999999}$$