Whakaoti i te 3x-8sqrt{x}-60=0

$$3x-8 \sqrt{ x } -60=0$$

Whakaoti mō x

$$x=36$$

Ngā Upane Otinga

Me tāpiri te 60 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$3x-8\sqrt{x}=60$$

Me tango 3x mai i ngā taha e rua o te whārite.

$$-8\sqrt{x}=60-3x$$

Pūruatia ngā taha e rua o te whārite.

$$\left(-8\sqrt{x}\right)^{2}=\left(60-3x\right)^{2}$$

Whakarohaina te \left(-8\sqrt{x}\right)^{2}.

$$\left(-8\right)^{2}\left(\sqrt{x}\right)^{2}=\left(60-3x\right)^{2}$$

Tātaihia te -8 mā te pū o 2, kia riro ko 64.

$$64\left(\sqrt{x}\right)^{2}=\left(60-3x\right)^{2}$$

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

$$64x=\left(60-3x\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(60-3x\right)^{2}.

$$64x=3600-360x+9x^{2}$$

Me tāpiri te 360x ki ngā taha e rua.

$$64x+360x=3600+9x^{2}$$

Pahekotia te 64x me 360x, ka 424x.

$$424x=3600+9x^{2}$$

Tangohia te 9x^{2} mai i ngā taha e rua.

$$424x-9x^{2}=3600$$

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.

$$-9x^{2}+424x=3600$$

Me tango 3600 mai i ngā taha e rua o te whārite.

$$-9x^{2}+424x-3600=3600-3600$$

Mā te tango i te 3600 i a ia ake anō ka toe ko te 0.

$$-9x^{2}+424x-3600=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -9 mō a, 424 mō b, me -3600 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-424±\sqrt{424^{2}-4\left(-9\right)\left(-3600\right)}}{2\left(-9\right)}$$

Pūrua 424.

$$x=\frac{-424±\sqrt{179776-4\left(-9\right)\left(-3600\right)}}{2\left(-9\right)}$$

Whakareatia -4 ki te -9.

$$x=\frac{-424±\sqrt{179776+36\left(-3600\right)}}{2\left(-9\right)}$$

Whakareatia 36 ki te -3600.

$$x=\frac{-424±\sqrt{179776-129600}}{2\left(-9\right)}$$

Tāpiri 179776 ki te -129600.

$$x=\frac{-424±\sqrt{50176}}{2\left(-9\right)}$$

Tuhia te pūtakerua o te 50176.

$$x=\frac{-424±224}{2\left(-9\right)}$$

Whakareatia 2 ki te -9.

$$x=\frac{-424±224}{-18}$$

Nā, me whakaoti te whārite x=\frac{-424±224}{-18} ina he tāpiri te ±. Tāpiri -424 ki te 224.

$$x=-\frac{200}{-18}$$

Whakahekea te hautanga \frac{-200}{-18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{100}{9}$$

Nā, me whakaoti te whārite x=\frac{-424±224}{-18} ina he tango te ±. Tango 224 mai i -424.

$$x=-\frac{648}{-18}$$

Whakawehe -648 ki te -18.

$$x=36$$

Kua oti te whārite te whakatau.

$$x=\frac{100}{9} x=36$$

Whakakapia te \frac{100}{9} mō te x i te whārite 3x-8\sqrt{x}-60=0.

$$3\times \frac{100}{9}-8\sqrt{\frac{100}{9}}-60=0$$

Whakarūnātia. Ko te uara x=\frac{100}{9} kāore e ngata ana ki te whārite.

$$-\frac{160}{3}=0$$

Whakakapia te 36 mō te x i te whārite 3x-8\sqrt{x}-60=0.

$$3\times 36-8\sqrt{36}-60=0$$

Whakarūnātia. Ko te uara x=36 kua ngata te whārite.

$$0=0$$

Ko te whārite -8\sqrt{x}=60-3x he rongoā ahurei.

$$x=36$$