Whakaoti i te (x-2)(x+4)=7

$$( x - 2 ) ( x + 4 ) = 7$$

Whakaoti mō x

$$x=-5$$

$$x=3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x-2 ki te x+4 ka whakakotahi i ngā kupu rite.

$$x^{2}+2x-8=7$$

Tangohia te 7 mai i ngā taha e rua.

$$x^{2}+2x-8-7=0$$

Tangohia te 7 i te -8, ka -15.

$$x^{2}+2x-15=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 2 mō b, me -15 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2±\sqrt{2^{2}-4\left(-15\right)}}{2}$$

Pūrua 2.

$$x=\frac{-2±\sqrt{4-4\left(-15\right)}}{2}$$

Whakareatia -4 ki te -15.

$$x=\frac{-2±\sqrt{4+60}}{2}$$

Tāpiri 4 ki te 60.

$$x=\frac{-2±\sqrt{64}}{2}$$

Tuhia te pūtakerua o te 64.

$$x=\frac{-2±8}{2}$$

Nā, me whakaoti te whārite x=\frac{-2±8}{2} ina he tāpiri te ±. Tāpiri -2 ki te 8.

$$x=\frac{6}{2}$$

Whakawehe 6 ki te 2.

$$x=3$$

Nā, me whakaoti te whārite x=\frac{-2±8}{2} ina he tango te ±. Tango 8 mai i -2.

$$x=-\frac{10}{2}$$

Whakawehe -10 ki te 2.

$$x=-5$$

Kua oti te whārite te whakatau.

$$x=3 x=-5$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x-2 ki te x+4 ka whakakotahi i ngā kupu rite.

$$x^{2}+2x-8=7$$

Me tāpiri te 8 ki ngā taha e rua.

$$x^{2}+2x=7+8$$

Tāpirihia te 7 ki te 8, ka 15.

$$x^{2}+2x=15$$

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.

$$x^{2}+2x+1^{2}=15+1^{2}$$

Pūrua 1.

$$x^{2}+2x+1=15+1$$

Tāpiri 15 ki te 1.

$$x^{2}+2x+1=16$$

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}.

$$\left(x+1\right)^{2}=16$$

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

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{16}$$

Whakarūnātia.

$$x+1=4 x+1=-4$$

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

$$x=3 x=-5$$