Whakaoti i te x^2-0x^2+20x-2x-16=0

$$x ^ { 2 } - 0 x ^ { 2 } + 20 x - 2 x - 16 = 0$$

Whakaoti mō x (complex solution)

$$x=\sqrt{97}-9\approx 0.848857802$$

$$x=-\left(\sqrt{97}+9\right)\approx -18.848857802$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ko te tau i whakarea ki te kore ka hua ko te kore.

$$x^{2}-0+20x-2x-16=0$$

Pahekotia te 20x me -2x, ka 18x.

$$x^{2}-0+18x-16=0$$

Whakaraupapatia anō ngā kīanga tau.

$$x^{2}+18x-16=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 18 mō b, me -16 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-18±\sqrt{18^{2}-4\left(-16\right)}}{2}$$

Pūrua 18.

$$x=\frac{-18±\sqrt{324-4\left(-16\right)}}{2}$$

Whakareatia -4 ki te -16.

$$x=\frac{-18±\sqrt{324+64}}{2}$$

Tāpiri 324 ki te 64.

$$x=\frac{-18±\sqrt{388}}{2}$$

Tuhia te pūtakerua o te 388.

$$x=\frac{-18±2\sqrt{97}}{2}$$

Nā, me whakaoti te whārite x=\frac{-18±2\sqrt{97}}{2} ina he tāpiri te ±. Tāpiri -18 ki te 2\sqrt{97}.

$$x=\frac{2\sqrt{97}-18}{2}$$

Whakawehe -18+2\sqrt{97} ki te 2.

$$x=\sqrt{97}-9$$

Nā, me whakaoti te whārite x=\frac{-18±2\sqrt{97}}{2} ina he tango te ±. Tango 2\sqrt{97} mai i -18.

$$x=\frac{-2\sqrt{97}-18}{2}$$

Whakawehe -18-2\sqrt{97} ki te 2.

$$x=-\sqrt{97}-9$$

Kua oti te whārite te whakatau.

$$x=\sqrt{97}-9 x=-\sqrt{97}-9$$

Ngā Upane mō te Whakaoti i te Pūrua

Ko te tau i whakarea ki te kore ka hua ko te kore.

$$x^{2}-0+20x-2x-16=0$$

Pahekotia te 20x me -2x, ka 18x.

$$x^{2}-0+18x-16=0$$

Me tāpiri te 16 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$x^{2}-0+18x=16$$

Whakaraupapatia anō ngā kīanga tau.

$$x^{2}+18x=16$$

Whakawehea te 18, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 9. Nā, tāpiria te pūrua o te 9 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+18x+9^{2}=16+9^{2}$$

Pūrua 9.

$$x^{2}+18x+81=16+81$$

Tāpiri 16 ki te 81.

$$x^{2}+18x+81=97$$

Tauwehea x^{2}+18x+81. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+9\right)^{2}=97$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(x+9\right)^{2}}=\sqrt{97}$$

Whakarūnātia.

$$x+9=\sqrt{97} x+9=-\sqrt{97}$$

Me tango 9 mai i ngā taha e rua o te whārite.

$$x=\sqrt{97}-9 x=-\sqrt{97}-9$$

Whakaoti mō x

$$x=\sqrt{97}-9\approx 0.848857802$$

$$x=-\sqrt{97}-9\approx -18.848857802$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ko te tau i whakarea ki te kore ka hua ko te kore.

$$x^{2}-0+20x-2x-16=0$$

Pahekotia te 20x me -2x, ka 18x.

$$x^{2}-0+18x-16=0$$

Whakaraupapatia anō ngā kīanga tau.

$$x^{2}+18x-16=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 18 mō b, me -16 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-18±\sqrt{18^{2}-4\left(-16\right)}}{2}$$

Pūrua 18.

$$x=\frac{-18±\sqrt{324-4\left(-16\right)}}{2}$$

Whakareatia -4 ki te -16.

$$x=\frac{-18±\sqrt{324+64}}{2}$$

Tāpiri 324 ki te 64.

$$x=\frac{-18±\sqrt{388}}{2}$$

Tuhia te pūtakerua o te 388.

$$x=\frac{-18±2\sqrt{97}}{2}$$

Nā, me whakaoti te whārite x=\frac{-18±2\sqrt{97}}{2} ina he tāpiri te ±. Tāpiri -18 ki te 2\sqrt{97}.

$$x=\frac{2\sqrt{97}-18}{2}$$

Whakawehe -18+2\sqrt{97} ki te 2.

$$x=\sqrt{97}-9$$

Nā, me whakaoti te whārite x=\frac{-18±2\sqrt{97}}{2} ina he tango te ±. Tango 2\sqrt{97} mai i -18.

$$x=\frac{-2\sqrt{97}-18}{2}$$

Whakawehe -18-2\sqrt{97} ki te 2.

$$x=-\sqrt{97}-9$$

Kua oti te whārite te whakatau.

$$x=\sqrt{97}-9 x=-\sqrt{97}-9$$

Ngā Upane mō te Whakaoti i te Pūrua

Ko te tau i whakarea ki te kore ka hua ko te kore.

$$x^{2}-0+20x-2x-16=0$$

Pahekotia te 20x me -2x, ka 18x.

$$x^{2}-0+18x-16=0$$

Me tāpiri te 16 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$x^{2}-0+18x=16$$

Whakaraupapatia anō ngā kīanga tau.

$$x^{2}+18x=16$$

Whakawehea te 18, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 9. Nā, tāpiria te pūrua o te 9 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+18x+9^{2}=16+9^{2}$$

Pūrua 9.

$$x^{2}+18x+81=16+81$$

Tāpiri 16 ki te 81.

$$x^{2}+18x+81=97$$

Tauwehea x^{2}+18x+81. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+9\right)^{2}=97$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(x+9\right)^{2}}=\sqrt{97}$$

Whakarūnātia.

$$x+9=\sqrt{97} x+9=-\sqrt{97}$$

Me tango 9 mai i ngā taha e rua o te whārite.

$$x=\sqrt{97}-9 x=-\sqrt{97}-9$$