Whakaoti i te (100+2x)(60+2x)=1200

$$(100+2x)(60+2x)=1200$$

Whakaoti mō x

$$x=-60$$

$$x=-20$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 100+2x ki te 60+2x ka whakakotahi i ngā kupu rite.

$$6000+320x+4x^{2}=1200$$

Tangohia te 1200 mai i ngā taha e rua.

$$6000+320x+4x^{2}-1200=0$$

Tangohia te 1200 i te 6000, ka 4800.

$$4800+320x+4x^{2}=0$$

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.

$$4x^{2}+320x+4800=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, 320 mō b, me 4800 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-320±\sqrt{320^{2}-4\times 4\times 4800}}{2\times 4}$$

Pūrua 320.

$$x=\frac{-320±\sqrt{102400-4\times 4\times 4800}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{-320±\sqrt{102400-16\times 4800}}{2\times 4}$$

Whakareatia -16 ki te 4800.

$$x=\frac{-320±\sqrt{102400-76800}}{2\times 4}$$

Tāpiri 102400 ki te -76800.

$$x=\frac{-320±\sqrt{25600}}{2\times 4}$$

Tuhia te pūtakerua o te 25600.

$$x=\frac{-320±160}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{-320±160}{8}$$

Nā, me whakaoti te whārite x=\frac{-320±160}{8} ina he tāpiri te ±. Tāpiri -320 ki te 160.

$$x=-\frac{160}{8}$$

Whakawehe -160 ki te 8.

$$x=-20$$

Nā, me whakaoti te whārite x=\frac{-320±160}{8} ina he tango te ±. Tango 160 mai i -320.

$$x=-\frac{480}{8}$$

Whakawehe -480 ki te 8.

$$x=-60$$

Kua oti te whārite te whakatau.

$$x=-20 x=-60$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 100+2x ki te 60+2x ka whakakotahi i ngā kupu rite.

$$6000+320x+4x^{2}=1200$$

Tangohia te 6000 mai i ngā taha e rua.

$$320x+4x^{2}=1200-6000$$

Tangohia te 6000 i te 1200, ka -4800.

$$320x+4x^{2}=-4800$$

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.

$$4x^{2}+320x=-4800$$

Whakawehea ngā taha e rua ki te 4.

$$\frac{4x^{2}+320x}{4}=-\frac{4800}{4}$$

Mā te whakawehe ki te 4 ka wetekia te whakareanga ki te 4.

$$x^{2}+\frac{320}{4}x=-\frac{4800}{4}$$

Whakawehe 320 ki te 4.

$$x^{2}+80x=-\frac{4800}{4}$$

Whakawehe -4800 ki te 4.

$$x^{2}+80x=-1200$$

Whakawehea te 80, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 40. Nā, tāpiria te pūrua o te 40 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+80x+40^{2}=-1200+40^{2}$$

Pūrua 40.

$$x^{2}+80x+1600=-1200+1600$$

Tāpiri -1200 ki te 1600.

$$x^{2}+80x+1600=400$$

Tauwehea x^{2}+80x+1600. 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}.

$$\left(x+40\right)^{2}=400$$

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

$$\sqrt{\left(x+40\right)^{2}}=\sqrt{400}$$

Whakarūnātia.

$$x+40=20 x+40=-20$$

Me tango 40 mai i ngā taha e rua o te whārite.

$$x=-20 x=-60$$