Whakaoti i te 75*18=(75+x)(18-x)

$$75 \times 18 = ( 75 + x ) ( 18 - x )$$

Whakaoti mō x

$$x=-57$$

$$x=0$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 75 ki te 18, ka 1350.

$$1350=\left(75+x\right)\left(18-x\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 75+x ki te 18-x ka whakakotahi i ngā kupu rite.

$$1350=1350-57x-x^{2}$$

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

$$1350-57x-x^{2}=1350$$

Tangohia te 1350 mai i ngā taha e rua.

$$1350-57x-x^{2}-1350=0$$

Tangohia te 1350 i te 1350, ka 0.

$$-57x-x^{2}=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$-x^{2}-57x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, -57 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-57\right)±\sqrt{\left(-57\right)^{2}}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te \left(-57\right)^{2}.

$$x=\frac{-\left(-57\right)±57}{2\left(-1\right)}$$

Ko te tauaro o -57 ko 57.

$$x=\frac{57±57}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{57±57}{-2}$$

Nā, me whakaoti te whārite x=\frac{57±57}{-2} ina he tāpiri te ±. Tāpiri 57 ki te 57.

$$x=\frac{114}{-2}$$

Whakawehe 114 ki te -2.

$$x=-57$$

Nā, me whakaoti te whārite x=\frac{57±57}{-2} ina he tango te ±. Tango 57 mai i 57.

$$x=\frac{0}{-2}$$

Whakawehe 0 ki te -2.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=-57 x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te 75 ki te 18, ka 1350.

$$1350=\left(75+x\right)\left(18-x\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 75+x ki te 18-x ka whakakotahi i ngā kupu rite.

$$1350=1350-57x-x^{2}$$

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

$$1350-57x-x^{2}=1350$$

Tangohia te 1350 mai i ngā taha e rua.

$$-57x-x^{2}=1350-1350$$

Tangohia te 1350 i te 1350, ka 0.

$$-57x-x^{2}=0$$

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$-x^{2}-57x=0$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}-57x}{-1}=\frac{0}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$x^{2}+\left(-\frac{57}{-1}\right)x=\frac{0}{-1}$$

Whakawehe -57 ki te -1.

$$x^{2}+57x=\frac{0}{-1}$$

Whakawehe 0 ki te -1.

$$x^{2}+57x=0$$

Whakawehea te 57, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{57}{2}. Nā, tāpiria te pūrua o te \frac{57}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+57x+\left(\frac{57}{2}\right)^{2}=\left(\frac{57}{2}\right)^{2}$$

Pūruatia \frac{57}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+57x+\frac{3249}{4}=\frac{3249}{4}$$

Tauwehea x^{2}+57x+\frac{3249}{4}. 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}.

$$\left(x+\frac{57}{2}\right)^{2}=\frac{3249}{4}$$

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

$$\sqrt{\left(x+\frac{57}{2}\right)^{2}}=\sqrt{\frac{3249}{4}}$$

Whakarūnātia.

$$x+\frac{57}{2}=\frac{57}{2} x+\frac{57}{2}=-\frac{57}{2}$$

Me tango \frac{57}{2} mai i ngā taha e rua o te whārite.

$$x=0 x=-57$$