Whakaoti i te 4x+sqrt{x}-6=0

$$4x+ \sqrt{ x } -6=0$$

Whakaoti mō x

$$x = \frac{49 - \sqrt{97}}{32} \approx 1.223473194$$

Ngā Upane Otinga

Me tango 4x-6 mai i ngā taha e rua o te whārite.

$$\sqrt{x}=-\left(4x-6\right)$$

Hei kimi i te tauaro o 4x-6, kimihia te tauaro o ia taurangi.

$$\sqrt{x}=-4x-\left(-6\right)$$

Ko te tauaro o -6 ko 6.

$$\sqrt{x}=-4x+6$$

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{x}\right)^{2}=\left(-4x+6\right)^{2}$$

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

$$x=\left(-4x+6\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(-4x+6\right)^{2}.

$$x=16x^{2}-48x+36$$

Tangohia te 16x^{2} mai i ngā taha e rua.

$$x-16x^{2}=-48x+36$$

Me tāpiri te 48x ki ngā taha e rua.

$$x-16x^{2}+48x=36$$

Pahekotia te x me 48x, ka 49x.

$$49x-16x^{2}=36$$

Tangohia te 36 mai i ngā taha e rua.

$$49x-16x^{2}-36=0$$

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.

$$-16x^{2}+49x-36=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -16 mō a, 49 mō b, me -36 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-49±\sqrt{49^{2}-4\left(-16\right)\left(-36\right)}}{2\left(-16\right)}$$

Pūrua 49.

$$x=\frac{-49±\sqrt{2401-4\left(-16\right)\left(-36\right)}}{2\left(-16\right)}$$

Whakareatia -4 ki te -16.

$$x=\frac{-49±\sqrt{2401+64\left(-36\right)}}{2\left(-16\right)}$$

Whakareatia 64 ki te -36.

$$x=\frac{-49±\sqrt{2401-2304}}{2\left(-16\right)}$$

Tāpiri 2401 ki te -2304.

$$x=\frac{-49±\sqrt{97}}{2\left(-16\right)}$$

Whakareatia 2 ki te -16.

$$x=\frac{-49±\sqrt{97}}{-32}$$

Nā, me whakaoti te whārite x=\frac{-49±\sqrt{97}}{-32} ina he tāpiri te ±. Tāpiri -49 ki te \sqrt{97}.

$$x=\frac{\sqrt{97}-49}{-32}$$

Whakawehe -49+\sqrt{97} ki te -32.

$$x=\frac{49-\sqrt{97}}{32}$$

Nā, me whakaoti te whārite x=\frac{-49±\sqrt{97}}{-32} ina he tango te ±. Tango \sqrt{97} mai i -49.

$$x=\frac{-\sqrt{97}-49}{-32}$$

Whakawehe -49-\sqrt{97} ki te -32.

$$x=\frac{\sqrt{97}+49}{32}$$

Kua oti te whārite te whakatau.

$$x=\frac{49-\sqrt{97}}{32} x=\frac{\sqrt{97}+49}{32}$$

Whakakapia te \frac{49-\sqrt{97}}{32} mō te x i te whārite 4x+\sqrt{x}-6=0.

$$4\times \frac{49-\sqrt{97}}{32}+\sqrt{\frac{49-\sqrt{97}}{32}}-6=0$$

Whakarūnātia. Ko te uara x=\frac{49-\sqrt{97}}{32} kua ngata te whārite.

$$0=0$$

Whakakapia te \frac{\sqrt{97}+49}{32} mō te x i te whārite 4x+\sqrt{x}-6=0.

$$4\times \frac{\sqrt{97}+49}{32}+\sqrt{\frac{\sqrt{97}+49}{32}}-6=0$$

Whakarūnātia. Ko te uara x=\frac{\sqrt{97}+49}{32} kāore e ngata ana ki te whārite.

$$\frac{1}{4}\times 97^{\frac{1}{2}}+\frac{1}{4}=0$$

Ko te whārite \sqrt{x}=6-4x he rongoā ahurei.

$$x=\frac{49-\sqrt{97}}{32}$$