Whakaoti i te 3x+sqrt{6x+4}=38

$$3x+ \sqrt{ 6x+4 } = 38$$

Whakaoti mō x

$$x=10$$

Ngā Upane Otinga

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

$$\sqrt{6x+4}=38-3x$$

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{6x+4}\right)^{2}=\left(38-3x\right)^{2}$$

Tātaihia te \sqrt{6x+4} mā te pū o 2, kia riro ko 6x+4.

$$6x+4=\left(38-3x\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(38-3x\right)^{2}.

$$6x+4=1444-228x+9x^{2}$$

Tangohia te 1444 mai i ngā taha e rua.

$$6x+4-1444=-228x+9x^{2}$$

Tangohia te 1444 i te 4, ka -1440.

$$6x-1440=-228x+9x^{2}$$

Me tāpiri te 228x ki ngā taha e rua.

$$6x-1440+228x=9x^{2}$$

Pahekotia te 6x me 228x, ka 234x.

$$234x-1440=9x^{2}$$

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

$$234x-1440-9x^{2}=0$$

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.

$$-9x^{2}+234x-1440=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -9 mō a, 234 mō b, me -1440 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-234±\sqrt{234^{2}-4\left(-9\right)\left(-1440\right)}}{2\left(-9\right)}$$

Pūrua 234.

$$x=\frac{-234±\sqrt{54756-4\left(-9\right)\left(-1440\right)}}{2\left(-9\right)}$$

Whakareatia -4 ki te -9.

$$x=\frac{-234±\sqrt{54756+36\left(-1440\right)}}{2\left(-9\right)}$$

Whakareatia 36 ki te -1440.

$$x=\frac{-234±\sqrt{54756-51840}}{2\left(-9\right)}$$

Tāpiri 54756 ki te -51840.

$$x=\frac{-234±\sqrt{2916}}{2\left(-9\right)}$$

Tuhia te pūtakerua o te 2916.

$$x=\frac{-234±54}{2\left(-9\right)}$$

Whakareatia 2 ki te -9.

$$x=\frac{-234±54}{-18}$$

Nā, me whakaoti te whārite x=\frac{-234±54}{-18} ina he tāpiri te ±. Tāpiri -234 ki te 54.

$$x=-\frac{180}{-18}$$

Whakawehe -180 ki te -18.

$$x=10$$

Nā, me whakaoti te whārite x=\frac{-234±54}{-18} ina he tango te ±. Tango 54 mai i -234.

$$x=-\frac{288}{-18}$$

Whakawehe -288 ki te -18.

$$x=16$$

Kua oti te whārite te whakatau.

$$x=10 x=16$$

Whakakapia te 10 mō te x i te whārite 3x+\sqrt{6x+4}=38.

$$3\times 10+\sqrt{6\times 10+4}=38$$

Whakarūnātia. Ko te uara x=10 kua ngata te whārite.

$$38=38$$

Whakakapia te 16 mō te x i te whārite 3x+\sqrt{6x+4}=38.

$$3\times 16+\sqrt{6\times 16+4}=38$$

Whakarūnātia. Ko te uara x=16 kāore e ngata ana ki te whārite.

$$58=38$$

Ko te whārite \sqrt{6x+4}=38-3x he rongoā ahurei.

$$x=10$$