Whakaoti i te (x+3)(x-5)=9

$$( x + 3 ) ( x - 5 ) = 9$$

Whakaoti mō x

$$x=-4$$

$$x=6$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x+3 ki te x-5 ka whakakotahi i ngā kupu rite.

$$x^{2}-2x-15=9$$

Tangohia te 9 mai i ngā taha e rua.

$$x^{2}-2x-15-9=0$$

Tangohia te 9 i te -15, ka -24.

$$x^{2}-2x-24=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -2 mō b, me -24 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-24\right)}}{2}$$

Pūrua -2.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\left(-24\right)}}{2}$$

Whakareatia -4 ki te -24.

$$x=\frac{-\left(-2\right)±\sqrt{4+96}}{2}$$

Tāpiri 4 ki te 96.

$$x=\frac{-\left(-2\right)±\sqrt{100}}{2}$$

Tuhia te pūtakerua o te 100.

$$x=\frac{-\left(-2\right)±10}{2}$$

Ko te tauaro o -2 ko 2.

$$x=\frac{2±10}{2}$$

Nā, me whakaoti te whārite x=\frac{2±10}{2} ina he tāpiri te ±. Tāpiri 2 ki te 10.

$$x=\frac{12}{2}$$

Whakawehe 12 ki te 2.

$$x=6$$

Nā, me whakaoti te whārite x=\frac{2±10}{2} ina he tango te ±. Tango 10 mai i 2.

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

Whakawehe -8 ki te 2.

$$x=-4$$

Kua oti te whārite te whakatau.

$$x=6 x=-4$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x+3 ki te x-5 ka whakakotahi i ngā kupu rite.

$$x^{2}-2x-15=9$$

Me tāpiri te 15 ki ngā taha e rua.

$$x^{2}-2x=9+15$$

Tāpirihia te 9 ki te 15, ka 24.

$$x^{2}-2x=24$$

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.

$$x^{2}-2x+1=24+1$$

Tāpiri 24 ki te 1.

$$x^{2}-2x+1=25$$

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}.

$$\left(x-1\right)^{2}=25$$

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

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{25}$$

Whakarūnātia.

$$x-1=5 x-1=-5$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$x=6 x=-4$$