Whakaoti i te 96=left(x+15right)left(x+5right)

$$96 = \left( x+15 \right) \left( x+5 \right)$$

Whakaoti mō x

$$x=-21$$

$$x=1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x+15 ki te x+5 ka whakakotahi i ngā kupu rite.

$$96=x^{2}+20x+75$$

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

$$x^{2}+20x+75=96$$

Tangohia te 96 mai i ngā taha e rua.

$$x^{2}+20x+75-96=0$$

Tangohia te 96 i te 75, ka -21.

$$x^{2}+20x-21=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 20 mō b, me -21 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-20±\sqrt{20^{2}-4\left(-21\right)}}{2}$$

Pūrua 20.

$$x=\frac{-20±\sqrt{400-4\left(-21\right)}}{2}$$

Whakareatia -4 ki te -21.

$$x=\frac{-20±\sqrt{400+84}}{2}$$

Tāpiri 400 ki te 84.

$$x=\frac{-20±\sqrt{484}}{2}$$

Tuhia te pūtakerua o te 484.

$$x=\frac{-20±22}{2}$$

Nā, me whakaoti te whārite x=\frac{-20±22}{2} ina he tāpiri te ±. Tāpiri -20 ki te 22.

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

Whakawehe 2 ki te 2.

$$x=1$$

Nā, me whakaoti te whārite x=\frac{-20±22}{2} ina he tango te ±. Tango 22 mai i -20.

$$x=-\frac{42}{2}$$

Whakawehe -42 ki te 2.

$$x=-21$$

Kua oti te whārite te whakatau.

$$x=1 x=-21$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x+15 ki te x+5 ka whakakotahi i ngā kupu rite.

$$96=x^{2}+20x+75$$

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

$$x^{2}+20x+75=96$$

Tangohia te 75 mai i ngā taha e rua.

$$x^{2}+20x=96-75$$

Tangohia te 75 i te 96, ka 21.

$$x^{2}+20x=21$$

Whakawehea te 20, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 10. Nā, tāpiria te pūrua o te 10 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+20x+10^{2}=21+10^{2}$$

Pūrua 10.

$$x^{2}+20x+100=21+100$$

Tāpiri 21 ki te 100.

$$x^{2}+20x+100=121$$

Tauwehea x^{2}+20x+100. 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}.

$$\left(x+10\right)^{2}=121$$

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

$$\sqrt{\left(x+10\right)^{2}}=\sqrt{121}$$

Whakarūnātia.

$$x+10=11 x+10=-11$$

Me tango 10 mai i ngā taha e rua o te whārite.

$$x=1 x=-21$$