Whakaoti i te (20-3x)(4-x)=28

$$(20-3x)(4-x)=28$$

Whakaoti mō x

$$x=2$$

$$x = \frac{26}{3} = 8\frac{2}{3} \approx 8.666666667$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 20-3x ki te 4-x ka whakakotahi i ngā kupu rite.

$$80-32x+3x^{2}=28$$

Tangohia te 28 mai i ngā taha e rua.

$$80-32x+3x^{2}-28=0$$

Tangohia te 28 i te 80, ka 52.

$$52-32x+3x^{2}=0$$

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.

$$3x^{2}-32x+52=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, -32 mō b, me 52 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-32\right)±\sqrt{\left(-32\right)^{2}-4\times 3\times 52}}{2\times 3}$$

Pūrua -32.

$$x=\frac{-\left(-32\right)±\sqrt{1024-4\times 3\times 52}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-32\right)±\sqrt{1024-12\times 52}}{2\times 3}$$

Whakareatia -12 ki te 52.

$$x=\frac{-\left(-32\right)±\sqrt{1024-624}}{2\times 3}$$

Tāpiri 1024 ki te -624.

$$x=\frac{-\left(-32\right)±\sqrt{400}}{2\times 3}$$

Tuhia te pūtakerua o te 400.

$$x=\frac{-\left(-32\right)±20}{2\times 3}$$

Ko te tauaro o -32 ko 32.

$$x=\frac{32±20}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{32±20}{6}$$

Nā, me whakaoti te whārite x=\frac{32±20}{6} ina he tāpiri te ±. Tāpiri 32 ki te 20.

$$x=\frac{52}{6}$$

Whakahekea te hautanga \frac{52}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{26}{3}$$

Nā, me whakaoti te whārite x=\frac{32±20}{6} ina he tango te ±. Tango 20 mai i 32.

$$x=\frac{12}{6}$$

Whakawehe 12 ki te 6.

$$x=2$$

Kua oti te whārite te whakatau.

$$x=\frac{26}{3} x=2$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 20-3x ki te 4-x ka whakakotahi i ngā kupu rite.

$$80-32x+3x^{2}=28$$

Tangohia te 80 mai i ngā taha e rua.

$$-32x+3x^{2}=28-80$$

Tangohia te 80 i te 28, ka -52.

$$-32x+3x^{2}=-52$$

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.

$$3x^{2}-32x=-52$$

Whakawehea ngā taha e rua ki te 3.

$$\frac{3x^{2}-32x}{3}=-\frac{52}{3}$$

Mā te whakawehe ki te 3 ka wetekia te whakareanga ki te 3.

$$x^{2}-\frac{32}{3}x=-\frac{52}{3}$$

Whakawehea te -\frac{32}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{16}{3}. Nā, tāpiria te pūrua o te -\frac{16}{3} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{32}{3}x+\left(-\frac{16}{3}\right)^{2}=-\frac{52}{3}+\left(-\frac{16}{3}\right)^{2}$$

Pūruatia -\frac{16}{3} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{32}{3}x+\frac{256}{9}=-\frac{52}{3}+\frac{256}{9}$$

Tāpiri -\frac{52}{3} ki te \frac{256}{9} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}-\frac{32}{3}x+\frac{256}{9}=\frac{100}{9}$$

Tauwehea x^{2}-\frac{32}{3}x+\frac{256}{9}. 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}.

$$\left(x-\frac{16}{3}\right)^{2}=\frac{100}{9}$$

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

$$\sqrt{\left(x-\frac{16}{3}\right)^{2}}=\sqrt{\frac{100}{9}}$$

Whakarūnātia.

$$x-\frac{16}{3}=\frac{10}{3} x-\frac{16}{3}=-\frac{10}{3}$$

Me tāpiri \frac{16}{3} ki ngā taha e rua o te whārite.

$$x=\frac{26}{3} x=2$$