Whakaoti i te 15(15+17)=x(x+14)

$$15(15+17)=x(x+14)$$

Whakaoti mō x

$$x=-30$$

$$x=16$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tāpirihia te 15 ki te 17, ka 32.

$$15\times 32=x\left(x+14\right)$$

Whakareatia te 15 ki te 32, ka 480.

$$480=x\left(x+14\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x+14.

$$480=x^{2}+14x$$

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

$$x^{2}+14x=480$$

Tangohia te 480 mai i ngā taha e rua.

$$x^{2}+14x-480=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 14 mō b, me -480 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-14±\sqrt{14^{2}-4\left(-480\right)}}{2}$$

Pūrua 14.

$$x=\frac{-14±\sqrt{196-4\left(-480\right)}}{2}$$

Whakareatia -4 ki te -480.

$$x=\frac{-14±\sqrt{196+1920}}{2}$$

Tāpiri 196 ki te 1920.

$$x=\frac{-14±\sqrt{2116}}{2}$$

Tuhia te pūtakerua o te 2116.

$$x=\frac{-14±46}{2}$$

Nā, me whakaoti te whārite x=\frac{-14±46}{2} ina he tāpiri te ±. Tāpiri -14 ki te 46.

$$x=\frac{32}{2}$$

Whakawehe 32 ki te 2.

$$x=16$$

Nā, me whakaoti te whārite x=\frac{-14±46}{2} ina he tango te ±. Tango 46 mai i -14.

$$x=-\frac{60}{2}$$

Whakawehe -60 ki te 2.

$$x=-30$$

Kua oti te whārite te whakatau.

$$x=16 x=-30$$

Ngā Upane mō te Whakaoti i te Pūrua

Tāpirihia te 15 ki te 17, ka 32.

$$15\times 32=x\left(x+14\right)$$

Whakareatia te 15 ki te 32, ka 480.

$$480=x\left(x+14\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x+14.

$$480=x^{2}+14x$$

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

$$x^{2}+14x=480$$

Whakawehea te 14, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 7. Nā, tāpiria te pūrua o te 7 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+14x+7^{2}=480+7^{2}$$

Pūrua 7.

$$x^{2}+14x+49=480+49$$

Tāpiri 480 ki te 49.

$$x^{2}+14x+49=529$$

Tauwehea x^{2}+14x+49. 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}.

$$\left(x+7\right)^{2}=529$$

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

$$\sqrt{\left(x+7\right)^{2}}=\sqrt{529}$$

Whakarūnātia.

$$x+7=23 x+7=-23$$

Me tango 7 mai i ngā taha e rua o te whārite.

$$x=16 x=-30$$