Whakaoti i te (x-1)(x+3)=5

$$(x-1)(x+3)=5$$

Whakaoti mō x

$$x=-4$$

$$x=2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x-1 ki te x+3 ka whakakotahi i ngā kupu rite.

$$x^{2}+2x-3=5$$

Tangohia te 5 mai i ngā taha e rua.

$$x^{2}+2x-3-5=0$$

Tangohia te 5 i te -3, ka -8.

$$x^{2}+2x-8=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 2 mō b, me -8 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2±\sqrt{2^{2}-4\left(-8\right)}}{2}$$

Pūrua 2.

$$x=\frac{-2±\sqrt{4-4\left(-8\right)}}{2}$$

Whakareatia -4 ki te -8.

$$x=\frac{-2±\sqrt{4+32}}{2}$$

Tāpiri 4 ki te 32.

$$x=\frac{-2±\sqrt{36}}{2}$$

Tuhia te pūtakerua o te 36.

$$x=\frac{-2±6}{2}$$

Nā, me whakaoti te whārite x=\frac{-2±6}{2} ina he tāpiri te ±. Tāpiri -2 ki te 6.

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

Whakawehe 4 ki te 2.

$$x=2$$

Nā, me whakaoti te whārite x=\frac{-2±6}{2} ina he tango te ±. Tango 6 mai i -2.

$$x=-\frac{8}{2}$$

Whakawehe -8 ki te 2.

$$x=-4$$

Kua oti te whārite te whakatau.

$$x=2 x=-4$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x-1 ki te x+3 ka whakakotahi i ngā kupu rite.

$$x^{2}+2x-3=5$$

Me tāpiri te 3 ki ngā taha e rua.

$$x^{2}+2x=5+3$$

Tāpirihia te 5 ki te 3, ka 8.

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

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.

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

Pūrua 1.

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

Tāpiri 8 ki te 1.

$$x^{2}+2x+1=9$$

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}.

$$\left(x+1\right)^{2}=9$$

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

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{9}$$

Whakarūnātia.

$$x+1=3 x+1=-3$$

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

$$x=2 x=-4$$