Whakaoti i te 30x-16sqrt{x}+2=0

$$30x-16 \sqrt{ x } +2=0$$

Whakaoti mō x

$$x=\frac{1}{9}\approx 0.111111111$$

$$x=\frac{1}{25}=0.04$$

Ngā Upane Otinga

Tangohia te 2 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$30x-16\sqrt{x}=-2$$

Me tango 30x mai i ngā taha e rua o te whārite.

$$-16\sqrt{x}=-2-30x$$

Pūruatia ngā taha e rua o te whārite.

$$\left(-16\sqrt{x}\right)^{2}=\left(-2-30x\right)^{2}$$

Whakarohaina te \left(-16\sqrt{x}\right)^{2}.

$$\left(-16\right)^{2}\left(\sqrt{x}\right)^{2}=\left(-2-30x\right)^{2}$$

Tātaihia te -16 mā te pū o 2, kia riro ko 256.

$$256\left(\sqrt{x}\right)^{2}=\left(-2-30x\right)^{2}$$

Tātaihia te \sqrt{x} mā te pū o 2, kia riro ko x.

$$256x=\left(-2-30x\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(-2-30x\right)^{2}.

$$256x=4+120x+900x^{2}$$

Tangohia te 120x mai i ngā taha e rua.

$$256x-120x=4+900x^{2}$$

Pahekotia te 256x me -120x, ka 136x.

$$136x=4+900x^{2}$$

Tangohia te 900x^{2} mai i ngā taha e rua.

$$136x-900x^{2}=4$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$-900x^{2}+136x=4$$

Me tango 4 mai i ngā taha e rua o te whārite.

$$-900x^{2}+136x-4=4-4$$

Mā te tango i te 4 i a ia ake anō ka toe ko te 0.

$$-900x^{2}+136x-4=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -900 mō a, 136 mō b, me -4 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-136±\sqrt{136^{2}-4\left(-900\right)\left(-4\right)}}{2\left(-900\right)}$$

Pūrua 136.

$$x=\frac{-136±\sqrt{18496-4\left(-900\right)\left(-4\right)}}{2\left(-900\right)}$$

Whakareatia -4 ki te -900.

$$x=\frac{-136±\sqrt{18496+3600\left(-4\right)}}{2\left(-900\right)}$$

Whakareatia 3600 ki te -4.

$$x=\frac{-136±\sqrt{18496-14400}}{2\left(-900\right)}$$

Tāpiri 18496 ki te -14400.

$$x=\frac{-136±\sqrt{4096}}{2\left(-900\right)}$$

Tuhia te pūtakerua o te 4096.

$$x=\frac{-136±64}{2\left(-900\right)}$$

Whakareatia 2 ki te -900.

$$x=\frac{-136±64}{-1800}$$

Nā, me whakaoti te whārite x=\frac{-136±64}{-1800} ina he tāpiri te ±. Tāpiri -136 ki te 64.

$$x=-\frac{72}{-1800}$$

Whakahekea te hautanga \frac{-72}{-1800} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 72.

$$x=\frac{1}{25}$$

Nā, me whakaoti te whārite x=\frac{-136±64}{-1800} ina he tango te ±. Tango 64 mai i -136.

$$x=-\frac{200}{-1800}$$

Whakahekea te hautanga \frac{-200}{-1800} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 200.

$$x=\frac{1}{9}$$

Kua oti te whārite te whakatau.

$$x=\frac{1}{25} x=\frac{1}{9}$$

Whakakapia te \frac{1}{25} mō te x i te whārite 30x-16\sqrt{x}+2=0.

$$30\times \frac{1}{25}-16\sqrt{\frac{1}{25}}+2=0$$

Whakarūnātia. Ko te uara x=\frac{1}{25} kua ngata te whārite.

$$0=0$$

Whakakapia te \frac{1}{9} mō te x i te whārite 30x-16\sqrt{x}+2=0.

$$30\times \frac{1}{9}-16\sqrt{\frac{1}{9}}+2=0$$

Whakarūnātia. Ko te uara x=\frac{1}{9} kua ngata te whārite.

$$0=0$$

Rārangihia ngā rongoā katoa o -16\sqrt{x}=-30x-2.

$$x=\frac{1}{25} x=\frac{1}{9}$$