Datrys -500000x^2+45x-9*10^-6=0

$$-500000 { x }^{ 2 } +45x-9 \times { 10 }^{ -6 } = 0$$

Datrys ar gyfer x

$$x=\frac{3\sqrt{223}}{1000000}+\frac{9}{200000}\approx 0.0000898$$

$$x=-\frac{3\sqrt{223}}{1000000}+\frac{9}{200000}\approx 0.0000002$$

Camau gan Ddefnyddio’r Fformiwla Cwadratig

Cyfrifo 10 i bŵer -6 a chael \frac{1}{1000000}.

$$-500000x^{2}+45x-9\times \frac{1}{1000000}=0$$

Lluosi 9 a \frac{1}{1000000} i gael \frac{9}{1000000}.

$$-500000x^{2}+45x-\frac{9}{1000000}=0$$

Mae’r hafaliad hwn yn y ffurf safonol: ax^{2}+bx+c=0. Amnewidiwch -500000 am a, 45 am b, a -\frac{9}{1000000} am c yn y fformiwla gwadratig, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-45±\sqrt{45^{2}-4\left(-500000\right)\left(-\frac{9}{1000000}\right)}}{2\left(-500000\right)}$$

Sgwâr 45.

$$x=\frac{-45±\sqrt{2025-4\left(-500000\right)\left(-\frac{9}{1000000}\right)}}{2\left(-500000\right)}$$

Lluoswch -4 â -500000.

$$x=\frac{-45±\sqrt{2025+2000000\left(-\frac{9}{1000000}\right)}}{2\left(-500000\right)}$$

Lluoswch 2000000 â -\frac{9}{1000000}.

$$x=\frac{-45±\sqrt{2025-18}}{2\left(-500000\right)}$$

Adio 2025 at -18.

$$x=\frac{-45±\sqrt{2007}}{2\left(-500000\right)}$$

Cymryd isradd 2007.

$$x=\frac{-45±3\sqrt{223}}{2\left(-500000\right)}$$

Lluoswch 2 â -500000.

$$x=\frac{-45±3\sqrt{223}}{-1000000}$$

Datryswch yr hafaliad x=\frac{-45±3\sqrt{223}}{-1000000} pan fydd ± yn plws. Adio -45 at 3\sqrt{223}.

$$x=\frac{3\sqrt{223}-45}{-1000000}$$

Rhannwch -45+3\sqrt{223} â -1000000.

$$x=-\frac{3\sqrt{223}}{1000000}+\frac{9}{200000}$$

Datryswch yr hafaliad x=\frac{-45±3\sqrt{223}}{-1000000} pan fydd ± yn minws. Tynnu 3\sqrt{223} o -45.

$$x=\frac{-3\sqrt{223}-45}{-1000000}$$

Rhannwch -45-3\sqrt{223} â -1000000.

$$x=\frac{3\sqrt{223}}{1000000}+\frac{9}{200000}$$

Mae’r hafaliad wedi’i ddatrys nawr.

$$x=-\frac{3\sqrt{223}}{1000000}+\frac{9}{200000} x=\frac{3\sqrt{223}}{1000000}+\frac{9}{200000}$$

Camau ar Gyfer Cwblhau'r Sgwâr

Cyfrifo 10 i bŵer -6 a chael \frac{1}{1000000}.

$$-500000x^{2}+45x-9\times \frac{1}{1000000}=0$$

Lluosi 9 a \frac{1}{1000000} i gael \frac{9}{1000000}.

$$-500000x^{2}+45x-\frac{9}{1000000}=0$$

Ychwanegu \frac{9}{1000000} at y ddwy ochr. Mae adio unrhyw beth at sero yn cyrraedd ei swm ei hun.

$$-500000x^{2}+45x=\frac{9}{1000000}$$

Rhannu’r ddwy ochr â -500000.

$$\frac{-500000x^{2}+45x}{-500000}=\frac{\frac{9}{1000000}}{-500000}$$

Mae rhannu â -500000 yn dad-wneud lluosi â -500000.

$$x^{2}+\frac{45}{-500000}x=\frac{\frac{9}{1000000}}{-500000}$$

Lleihau'r ffracsiwn \frac{45}{-500000} i'r graddau lleiaf posib drwy dynnu a chanslo allan 5.

$$x^{2}-\frac{9}{100000}x=\frac{\frac{9}{1000000}}{-500000}$$

Rhannwch \frac{9}{1000000} â -500000.

$$x^{2}-\frac{9}{100000}x=-\frac{9}{500000000000}$$

Rhannwch -\frac{9}{100000}, cyfernod y term x, â 2 i gael -\frac{9}{200000}. Yna ychwanegwch sgwâr -\frac{9}{200000} at ddwy ochr yr hafaliad. Mae'r cam hwn yn gwneud ochr chwith yr hafaliad yn sgwâr perffaith.

$$x^{2}-\frac{9}{100000}x+\left(-\frac{9}{200000}\right)^{2}=-\frac{9}{500000000000}+\left(-\frac{9}{200000}\right)^{2}$$

Sgwariwch -\frac{9}{200000} drwy sgwario'r rhifiadur ag enwadur y ffracsiwn.

$$x^{2}-\frac{9}{100000}x+\frac{81}{40000000000}=-\frac{9}{500000000000}+\frac{81}{40000000000}$$

Adio -\frac{9}{500000000000} at \frac{81}{40000000000} drwy ddod o hyd i enwadur cyffredin ac ychwanegu’r rhifiaduron. Yna, lleihau’r ffracsiwn i’r termau isaf os yn bosibl.

$$x^{2}-\frac{9}{100000}x+\frac{81}{40000000000}=\frac{2007}{1000000000000}$$

Ffactora x^{2}-\frac{9}{100000}x+\frac{81}{40000000000}. 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}.

$$\left(x-\frac{9}{200000}\right)^{2}=\frac{2007}{1000000000000}$$

Cymrwch isradd dwy ochr yr hafaliad.

$$\sqrt{\left(x-\frac{9}{200000}\right)^{2}}=\sqrt{\frac{2007}{1000000000000}}$$

Symleiddio.

$$x-\frac{9}{200000}=\frac{3\sqrt{223}}{1000000} x-\frac{9}{200000}=-\frac{3\sqrt{223}}{1000000}$$

Adio \frac{9}{200000} at ddwy ochr yr hafaliad.

$$x=\frac{3\sqrt{223}}{1000000}+\frac{9}{200000} x=-\frac{3\sqrt{223}}{1000000}+\frac{9}{200000}$$