Whakaoti i te sqrt{x}=5x+3

$$\sqrt{ x } =5x+3$$

Whakaoti mō x (complex solution)

$$x=\frac{-29+\sqrt{59}i}{50}\approx -0.58+0.153622915i$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{x}\right)^{2}=\left(5x+3\right)^{2}$$

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

$$x=\left(5x+3\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(5x+3\right)^{2}.

$$x=25x^{2}+30x+9$$

Tangohia te 25x^{2} mai i ngā taha e rua.

$$x-25x^{2}=30x+9$$

Tangohia te 30x mai i ngā taha e rua.

$$x-25x^{2}-30x=9$$

Pahekotia te x me -30x, ka -29x.

$$-29x-25x^{2}=9$$

Tangohia te 9 mai i ngā taha e rua.

$$-29x-25x^{2}-9=0$$

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.

$$-25x^{2}-29x-9=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -25 mō a, -29 mō b, me -9 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-29\right)±\sqrt{\left(-29\right)^{2}-4\left(-25\right)\left(-9\right)}}{2\left(-25\right)}$$

Pūrua -29.

$$x=\frac{-\left(-29\right)±\sqrt{841-4\left(-25\right)\left(-9\right)}}{2\left(-25\right)}$$

Whakareatia -4 ki te -25.

$$x=\frac{-\left(-29\right)±\sqrt{841+100\left(-9\right)}}{2\left(-25\right)}$$

Whakareatia 100 ki te -9.

$$x=\frac{-\left(-29\right)±\sqrt{841-900}}{2\left(-25\right)}$$

Tāpiri 841 ki te -900.

$$x=\frac{-\left(-29\right)±\sqrt{-59}}{2\left(-25\right)}$$

Tuhia te pūtakerua o te -59.

$$x=\frac{-\left(-29\right)±\sqrt{59}i}{2\left(-25\right)}$$

Ko te tauaro o -29 ko 29.

$$x=\frac{29±\sqrt{59}i}{2\left(-25\right)}$$

Whakareatia 2 ki te -25.

$$x=\frac{29±\sqrt{59}i}{-50}$$

Nā, me whakaoti te whārite x=\frac{29±\sqrt{59}i}{-50} ina he tāpiri te ±. Tāpiri 29 ki te i\sqrt{59}.

$$x=\frac{29+\sqrt{59}i}{-50}$$

Whakawehe 29+i\sqrt{59} ki te -50.

$$x=\frac{-\sqrt{59}i-29}{50}$$

Nā, me whakaoti te whārite x=\frac{29±\sqrt{59}i}{-50} ina he tango te ±. Tango i\sqrt{59} mai i 29.

$$x=\frac{-\sqrt{59}i+29}{-50}$$

Whakawehe 29-i\sqrt{59} ki te -50.

$$x=\frac{-29+\sqrt{59}i}{50}$$

Kua oti te whārite te whakatau.

$$x=\frac{-\sqrt{59}i-29}{50} x=\frac{-29+\sqrt{59}i}{50}$$

Whakakapia te \frac{-\sqrt{59}i-29}{50} mō te x i te whārite \sqrt{x}=5x+3.

$$\sqrt{\frac{-\sqrt{59}i-29}{50}}=5\times \frac{-\sqrt{59}i-29}{50}+3$$

Whakarūnātia. Ko te uara x=\frac{-\sqrt{59}i-29}{50} kāore e ngata ana ki te whārite.

$$-\left(\frac{1}{10}-\frac{1}{10}i\times 59^{\frac{1}{2}}\right)=-\frac{1}{10}i\times 59^{\frac{1}{2}}+\frac{1}{10}$$

Whakakapia te \frac{-29+\sqrt{59}i}{50} mō te x i te whārite \sqrt{x}=5x+3.

$$\sqrt{\frac{-29+\sqrt{59}i}{50}}=5\times \frac{-29+\sqrt{59}i}{50}+3$$

Whakarūnātia. Ko te uara x=\frac{-29+\sqrt{59}i}{50} kua ngata te whārite.

$$\frac{1}{10}+\frac{1}{10}i\times 59^{\frac{1}{2}}=\frac{1}{10}+\frac{1}{10}i\times 59^{\frac{1}{2}}$$

Ko te whārite \sqrt{x}=5x+3 he rongoā ahurei.

$$x=\frac{-29+\sqrt{59}i}{50}$$