Datrys x^2/308-x=83176*10^-5

$$\frac{ { x }^{ 2 } }{ 308-x } = 83176 \times { 10 }^{ -5 }$$

Datrys ar gyfer x

$$x = \frac{\sqrt{160221897609} - 10397}{25000} \approx 15.595211036$$

$$x=\frac{-\sqrt{160221897609}-10397}{25000}\approx -16.426971036$$

Camau gan Ddefnyddio’r Fformiwla Cwadratig

All y newidyn x ddim fod yn hafal i 308 gan nad ydy rhannu â sero wedi’i ddiffinio. Lluoswch ddwy ochr yr hafaliad â -x+308.

$$x^{2}=83176\times 10^{-5}\left(-x+308\right)$$

Cyfrifo 10 i bŵer -5 a chael \frac{1}{100000}.

$$x^{2}=83176\times \frac{1}{100000}\left(-x+308\right)$$

Lluosi 83176 a \frac{1}{100000} i gael \frac{10397}{12500}.

$$x^{2}=\frac{10397}{12500}\left(-x+308\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi \frac{10397}{12500} â -x+308.

$$x^{2}=-\frac{10397}{12500}x+\frac{800569}{3125}$$

Ychwanegu \frac{10397}{12500}x at y ddwy ochr.

$$x^{2}+\frac{10397}{12500}x=\frac{800569}{3125}$$

Tynnu \frac{800569}{3125} o'r ddwy ochr.

$$x^{2}+\frac{10397}{12500}x-\frac{800569}{3125}=0$$

Mae’r hafaliad hwn yn y ffurf safonol: ax^{2}+bx+c=0. Amnewidiwch 1 am a, \frac{10397}{12500} am b, a -\frac{800569}{3125} am c yn y fformiwla gwadratig, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\frac{10397}{12500}±\sqrt{\left(\frac{10397}{12500}\right)^{2}-4\left(-\frac{800569}{3125}\right)}}{2}$$

Sgwariwch \frac{10397}{12500} drwy sgwario'r rhifiadur ag enwadur y ffracsiwn.

$$x=\frac{-\frac{10397}{12500}±\sqrt{\frac{108097609}{156250000}-4\left(-\frac{800569}{3125}\right)}}{2}$$

Lluoswch -4 â -\frac{800569}{3125}.

$$x=\frac{-\frac{10397}{12500}±\sqrt{\frac{108097609}{156250000}+\frac{3202276}{3125}}}{2}$$

Adio \frac{108097609}{156250000} at \frac{3202276}{3125} drwy ddod o hyd i enwadur cyffredin ac ychwanegu’r rhifiaduron. Yna, lleihau’r ffracsiwn i’r termau isaf os yn bosibl.

$$x=\frac{-\frac{10397}{12500}±\sqrt{\frac{160221897609}{156250000}}}{2}$$

Cymryd isradd \frac{160221897609}{156250000}.

$$x=\frac{-\frac{10397}{12500}±\frac{\sqrt{160221897609}}{12500}}{2}$$

Datryswch yr hafaliad x=\frac{-\frac{10397}{12500}±\frac{\sqrt{160221897609}}{12500}}{2} pan fydd ± yn plws. Adio -\frac{10397}{12500} at \frac{\sqrt{160221897609}}{12500}.

$$x=\frac{\sqrt{160221897609}-10397}{2\times 12500}$$

Rhannwch \frac{-10397+\sqrt{160221897609}}{12500} â 2.

$$x=\frac{\sqrt{160221897609}-10397}{25000}$$

Datryswch yr hafaliad x=\frac{-\frac{10397}{12500}±\frac{\sqrt{160221897609}}{12500}}{2} pan fydd ± yn minws. Tynnu \frac{\sqrt{160221897609}}{12500} o -\frac{10397}{12500}.

$$x=\frac{-\sqrt{160221897609}-10397}{2\times 12500}$$

Rhannwch \frac{-10397-\sqrt{160221897609}}{12500} â 2.

$$x=\frac{-\sqrt{160221897609}-10397}{25000}$$

Mae’r hafaliad wedi’i ddatrys nawr.

$$x=\frac{\sqrt{160221897609}-10397}{25000} x=\frac{-\sqrt{160221897609}-10397}{25000}$$

Camau ar Gyfer Cwblhau'r Sgwâr

All y newidyn x ddim fod yn hafal i 308 gan nad ydy rhannu â sero wedi’i ddiffinio. Lluoswch ddwy ochr yr hafaliad â -x+308.

$$x^{2}=83176\times 10^{-5}\left(-x+308\right)$$

Cyfrifo 10 i bŵer -5 a chael \frac{1}{100000}.

$$x^{2}=83176\times \frac{1}{100000}\left(-x+308\right)$$

Lluosi 83176 a \frac{1}{100000} i gael \frac{10397}{12500}.

$$x^{2}=\frac{10397}{12500}\left(-x+308\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi \frac{10397}{12500} â -x+308.

$$x^{2}=-\frac{10397}{12500}x+\frac{800569}{3125}$$

Ychwanegu \frac{10397}{12500}x at y ddwy ochr.

$$x^{2}+\frac{10397}{12500}x=\frac{800569}{3125}$$

Rhannwch \frac{10397}{12500}, cyfernod y term x, â 2 i gael \frac{10397}{25000}. Yna ychwanegwch sgwâr \frac{10397}{25000} at ddwy ochr yr hafaliad. Mae'r cam hwn yn gwneud ochr chwith yr hafaliad yn sgwâr perffaith.

$$x^{2}+\frac{10397}{12500}x+\left(\frac{10397}{25000}\right)^{2}=\frac{800569}{3125}+\left(\frac{10397}{25000}\right)^{2}$$

Sgwariwch \frac{10397}{25000} drwy sgwario'r rhifiadur ag enwadur y ffracsiwn.

$$x^{2}+\frac{10397}{12500}x+\frac{108097609}{625000000}=\frac{800569}{3125}+\frac{108097609}{625000000}$$

Adio \frac{800569}{3125} at \frac{108097609}{625000000} drwy ddod o hyd i enwadur cyffredin ac ychwanegu’r rhifiaduron. Yna, lleihau’r ffracsiwn i’r termau isaf os yn bosibl.

$$x^{2}+\frac{10397}{12500}x+\frac{108097609}{625000000}=\frac{160221897609}{625000000}$$

Ffactora x^{2}+\frac{10397}{12500}x+\frac{108097609}{625000000}. 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}.

$$\left(x+\frac{10397}{25000}\right)^{2}=\frac{160221897609}{625000000}$$

Cymrwch isradd dwy ochr yr hafaliad.

$$\sqrt{\left(x+\frac{10397}{25000}\right)^{2}}=\sqrt{\frac{160221897609}{625000000}}$$

Symleiddio.

$$x+\frac{10397}{25000}=\frac{\sqrt{160221897609}}{25000} x+\frac{10397}{25000}=-\frac{\sqrt{160221897609}}{25000}$$

Tynnu \frac{10397}{25000} o ddwy ochr yr hafaliad.

$$x=\frac{\sqrt{160221897609}-10397}{25000} x=\frac{-\sqrt{160221897609}-10397}{25000}$$