Datrys 50/17*9800+34*9800h=26500(h^2-8875^2)

$$\frac { 50 } { 17 } \times 9800 + 34 \times 9800 h = 26500 ( h ^ { 2 } - 8875 ^ { 2 } )$$

Datrys ar gyfer h

$$h=\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265}\approx 8881.289080421$$

$$h=-\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265}\approx -8868.715495515$$

Camau gan Ddefnyddio’r Fformiwla Cwadratig

Lluosi \frac{50}{17} a 9800 i gael \frac{490000}{17}.

$$\frac{490000}{17}+34\times 9800h=26500\left(h^{2}-8875^{2}\right)$$

Lluosi 34 a 9800 i gael 333200.

$$\frac{490000}{17}+333200h=26500\left(h^{2}-8875^{2}\right)$$

Cyfrifo 8875 i bŵer 2 a chael 78765625.

$$\frac{490000}{17}+333200h=26500\left(h^{2}-78765625\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi 26500 â h^{2}-78765625.

$$\frac{490000}{17}+333200h=26500h^{2}-2087289062500$$

Tynnu 26500h^{2} o'r ddwy ochr.

$$\frac{490000}{17}+333200h-26500h^{2}=-2087289062500$$

Ychwanegu 2087289062500 at y ddwy ochr.

$$\frac{490000}{17}+333200h-26500h^{2}[phone]=0$$

Adio \frac{490000}{17} a 2087289062500 i gael \frac{35483914552500}{17}.

$$\frac{35483914552500}{17}+333200h-26500h^{2}=0$$

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.

$$-26500h^{2}+333200h+\frac{35483914552500}{17}=0$$

Mae’r hafaliad hwn yn y ffurf safonol: ax^{2}+bx+c=0. Amnewidiwch -26500 am a, 333200 am b, a \frac{35483914552500}{17} am c yn y fformiwla gwadratig, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$h=\frac{-333200±\sqrt{333200^{2}-4\left(-26500\right)\times \frac{35483914552500}{17}}}{2\left(-26500\right)}$$

Sgwâr 333200.

$$h=\frac{-333200±\sqrt{111022240000-4\left(-26500\right)\times \frac{35483914552500}{17}}}{2\left(-26500\right)}$$

Lluoswch -4 â -26500.

$$h=\frac{-333200±\sqrt{111022240000+106000\times \frac{35483914552500}{17}}}{2\left(-26500\right)}$$

Lluoswch 106000 â \frac{35483914552500}{17}.

$$h=\frac{-333200±\sqrt{111022240000+\frac{3761294942565000000}{17}}}{2\left(-26500\right)}$$

Adio 111022240000 at \frac{3761294942565000000}{17}.

$$h=\frac{-333200±\sqrt{\frac{3761296829943080000}{17}}}{2\left(-26500\right)}$$

Cymryd isradd \frac{3761296829943080000}{17}.

$$h=\frac{-333200±\frac{200\sqrt{1598551152725809}}{17}}{2\left(-26500\right)}$$

Lluoswch 2 â -26500.

$$h=\frac{-333200±\frac{200\sqrt{1598551152725809}}{17}}{-53000}$$

Datryswch yr hafaliad h=\frac{-333200±\frac{200\sqrt{1598551152725809}}{17}}{-53000} pan fydd ± yn plws. Adio -333200 at \frac{200\sqrt{1598551152725809}}{17}.

$$h=\frac{\frac{200\sqrt{1598551152725809}}{17}-333200}{-53000}$$

Rhannwch -333200+\frac{200\sqrt{1598551152725809}}{17} â -53000.

$$h=-\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265}$$

Datryswch yr hafaliad h=\frac{-333200±\frac{200\sqrt{1598551152725809}}{17}}{-53000} pan fydd ± yn minws. Tynnu \frac{200\sqrt{1598551152725809}}{17} o -333200.

$$h=\frac{-\frac{200\sqrt{1598551152725809}}{17}-333200}{-53000}$$

Rhannwch -333200-\frac{200\sqrt{1598551152725809}}{17} â -53000.

$$h=\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265}$$

Mae’r hafaliad wedi’i ddatrys nawr.

$$h=-\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265} h=\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265}$$

Camau ar Gyfer Cwblhau'r Sgwâr

Lluosi \frac{50}{17} a 9800 i gael \frac{490000}{17}.

$$\frac{490000}{17}+34\times 9800h=26500\left(h^{2}-8875^{2}\right)$$

Lluosi 34 a 9800 i gael 333200.

$$\frac{490000}{17}+333200h=26500\left(h^{2}-8875^{2}\right)$$

Cyfrifo 8875 i bŵer 2 a chael 78765625.

$$\frac{490000}{17}+333200h=26500\left(h^{2}-78765625\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi 26500 â h^{2}-78765625.

$$\frac{490000}{17}+333200h=26500h^{2}-2087289062500$$

Tynnu 26500h^{2} o'r ddwy ochr.

$$\frac{490000}{17}+333200h-26500h^{2}=-2087289062500$$

Tynnu \frac{490000}{17} o'r ddwy ochr.

$$333200h-26500h^{2}=-2087289062500-\frac{490000}{17}$$

Tynnu \frac{490000}{17} o -2087289062500 i gael -\frac{35483914552500}{17}.

$$333200h-26500h^{2}=-\frac{35483914552500}{17}$$

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.

$$-26500h^{2}+333200h=-\frac{35483914552500}{17}$$

Rhannu’r ddwy ochr â -26500.

$$\frac{-26500h^{2}+333200h}{-26500}=-\frac{\frac{35483914552500}{17}}{-26500}$$

Mae rhannu â -26500 yn dad-wneud lluosi â -26500.

$$h^{2}+\frac{333200}{-26500}h=-\frac{\frac{35483914552500}{17}}{-26500}$$

Lleihau'r ffracsiwn \frac{333200}{-26500} i'r graddau lleiaf posib drwy dynnu a chanslo allan 100.

$$h^{2}-\frac{3332}{265}h=-\frac{\frac{35483914552500}{17}}{-26500}$$

Rhannwch -\frac{35483914552500}{17} â -26500.

$$h^{2}-\frac{3332}{265}h=\frac{70967829105}{901}$$

Rhannwch -\frac{3332}{265}, cyfernod y term x, â 2 i gael -\frac{1666}{265}. Yna ychwanegwch sgwâr -\frac{1666}{265} at ddwy ochr yr hafaliad. Mae'r cam hwn yn gwneud ochr chwith yr hafaliad yn sgwâr perffaith.

$$h^{2}-\frac{3332}{265}h+\left(-\frac{1666}{265}\right)^{2}=\frac{70967829105}{901}+\left(-\frac{1666}{265}\right)^{2}$$

Sgwariwch -\frac{1666}{265} drwy sgwario'r rhifiadur ag enwadur y ffracsiwn.

$$h^{2}-\frac{3332}{265}h+\frac{2775556}{70225}=\frac{70967829105}{901}+\frac{2775556}{70225}$$

Adio \frac{70967829105}{901} at \frac{2775556}{70225} drwy ddod o hyd i enwadur cyffredin ac ychwanegu’r rhifiaduron. Yna, lleihau’r ffracsiwn i’r termau isaf os yn bosibl.

$$h^{2}-\frac{3332}{265}h+\frac{2775556}{70225}=\frac{94032420748577}{1193825}$$

Ffactora h^{2}-\frac{3332}{265}h+\frac{2775556}{70225}. 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}.

$$\left(h-\frac{1666}{265}\right)^{2}=\frac{94032420748577}{1193825}$$

Cymrwch isradd dwy ochr yr hafaliad.

$$\sqrt{\left(h-\frac{1666}{265}\right)^{2}}=\sqrt{\frac{94032420748577}{1193825}}$$

Symleiddio.

$$h-\frac{1666}{265}=\frac{\sqrt{1598551152725809}}{4505} h-\frac{1666}{265}=-\frac{\sqrt{1598551152725809}}{4505}$$

Adio \frac{1666}{265} at ddwy ochr yr hafaliad.

$$h=\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265} h=-\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265}$$