Whakaoti i te 0=x^2+2x-7

$$0 = x ^ { 2 } + 2 x - 7$$

Whakaoti mō x

$$x=2\sqrt{2}-1\approx 1.828427125$$

$$x=-2\sqrt{2}-1\approx -3.828427125$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{2}+2x-7=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 2 mō b, me -7 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2±\sqrt{2^{2}-4\left(-7\right)}}{2}$$

Pūrua 2.

$$x=\frac{-2±\sqrt{4-4\left(-7\right)}}{2}$$

Whakareatia -4 ki te -7.

$$x=\frac{-2±\sqrt{4+28}}{2}$$

Tāpiri 4 ki te 28.

$$x=\frac{-2±\sqrt{32}}{2}$$

Tuhia te pūtakerua o te 32.

$$x=\frac{-2±4\sqrt{2}}{2}$$

Nā, me whakaoti te whārite x=\frac{-2±4\sqrt{2}}{2} ina he tāpiri te ±. Tāpiri -2 ki te 4\sqrt{2}.

$$x=\frac{4\sqrt{2}-2}{2}$$

Whakawehe 4\sqrt{2}-2 ki te 2.

$$x=2\sqrt{2}-1$$

Nā, me whakaoti te whārite x=\frac{-2±4\sqrt{2}}{2} ina he tango te ±. Tango 4\sqrt{2} mai i -2.

$$x=\frac{-4\sqrt{2}-2}{2}$$

Whakawehe -2-4\sqrt{2} ki te 2.

$$x=-2\sqrt{2}-1$$

Kua oti te whārite te whakatau.

$$x=2\sqrt{2}-1 x=-2\sqrt{2}-1$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{2}+2x-7=0$$

Me tāpiri te 7 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$x^{2}+2x=7$$

Whakawehea te 2, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 1. Nā, tāpiria te pūrua o te 1 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+2x+1^{2}=7+1^{2}$$

Pūrua 1.

$$x^{2}+2x+1=7+1$$

Tāpiri 7 ki te 1.

$$x^{2}+2x+1=8$$

Tauwehea x^{2}+2x+1. 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}.

$$\left(x+1\right)^{2}=8$$

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

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{8}$$

Whakarūnātia.

$$x+1=2\sqrt{2} x+1=-2\sqrt{2}$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$x=2\sqrt{2}-1 x=-2\sqrt{2}-1$$