Whakaoti i te 18-4.5x=64-32x+4x^2

$$18-4.5x=64-32x+4 { x }^{ 2 }$$

Whakaoti mō x

$$x=4$$

$$x=2.875$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 64 mai i ngā taha e rua.

$$18-4.5x-64=-32x+4x^{2}$$

Tangohia te 64 i te 18, ka -46.

$$-46-4.5x=-32x+4x^{2}$$

Me tāpiri te 32x ki ngā taha e rua.

$$-46-4.5x+32x=4x^{2}$$

Pahekotia te -4.5x me 32x, ka 27.5x.

$$-46+27.5x=4x^{2}$$

Tangohia te 4x^{2} mai i ngā taha e rua.

$$-46+27.5x-4x^{2}=0$$

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.

$$-4x^{2}+27.5x-46=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -4 mō a, 27.5 mō b, me -46 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-27.5±\sqrt{27.5^{2}-4\left(-4\right)\left(-46\right)}}{2\left(-4\right)}$$

Pūruatia 27.5 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-27.5±\sqrt{756.25-4\left(-4\right)\left(-46\right)}}{2\left(-4\right)}$$

Whakareatia -4 ki te -4.

$$x=\frac{-27.5±\sqrt{756.25+16\left(-46\right)}}{2\left(-4\right)}$$

Whakareatia 16 ki te -46.

$$x=\frac{-27.5±\sqrt{756.25-736}}{2\left(-4\right)}$$

Tāpiri 756.25 ki te -736.

$$x=\frac{-27.5±\sqrt{20.25}}{2\left(-4\right)}$$

Tuhia te pūtakerua o te 20.25.

$$x=\frac{-27.5±\frac{9}{2}}{2\left(-4\right)}$$

Whakareatia 2 ki te -4.

$$x=\frac{-27.5±\frac{9}{2}}{-8}$$

Nā, me whakaoti te whārite x=\frac{-27.5±\frac{9}{2}}{-8} ina he tāpiri te ±. Tāpiri -27.5 ki te \frac{9}{2} 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.

$$x=-\frac{23}{-8}$$

Whakawehe -23 ki te -8.

$$x=\frac{23}{8}$$

Nā, me whakaoti te whārite x=\frac{-27.5±\frac{9}{2}}{-8} ina he tango te ±. Tango \frac{9}{2} mai i -27.5 mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x=-\frac{32}{-8}$$

Whakawehe -32 ki te -8.

$$x=4$$

Kua oti te whārite te whakatau.

$$x=\frac{23}{8} x=4$$

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te 32x ki ngā taha e rua.

$$18-4.5x+32x=64+4x^{2}$$

Pahekotia te -4.5x me 32x, ka 27.5x.

$$18+27.5x=64+4x^{2}$$

Tangohia te 4x^{2} mai i ngā taha e rua.

$$18+27.5x-4x^{2}=64$$

Tangohia te 18 mai i ngā taha e rua.

$$27.5x-4x^{2}=64-18$$

Tangohia te 18 i te 64, ka 46.

$$27.5x-4x^{2}=46$$

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.

$$-4x^{2}+27.5x=46$$

Whakawehea ngā taha e rua ki te -4.

$$\frac{-4x^{2}+27.5x}{-4}=\frac{46}{-4}$$

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

$$x^{2}+\frac{27.5}{-4}x=\frac{46}{-4}$$

Whakawehe 27.5 ki te -4.

$$x^{2}-6.875x=\frac{46}{-4}$$

Whakahekea te hautanga \frac{46}{-4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}-6.875x=-\frac{23}{2}$$

Whakawehea te -6.875, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -3.4375. Nā, tāpiria te pūrua o te -3.4375 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-6.875x+\left(-3.4375\right)^{2}=-\frac{23}{2}+\left(-3.4375\right)^{2}$$

Pūruatia -3.4375 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-6.875x+11.81640625=-\frac{23}{2}+11.81640625$$

Tāpiri -\frac{23}{2} ki te 11.81640625 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.

$$x^{2}-6.875x+11.81640625=\frac{81}{256}$$

Tauwehea x^{2}-6.875x+11.81640625. 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}.

$$\left(x-3.4375\right)^{2}=\frac{81}{256}$$

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

$$\sqrt{\left(x-3.4375\right)^{2}}=\sqrt{\frac{81}{256}}$$

Whakarūnātia.

$$x-3.4375=\frac{9}{16} x-3.4375=-\frac{9}{16}$$

Me tāpiri 3.4375 ki ngā taha e rua o te whārite.

$$x=4 x=\frac{23}{8}$$