Whakaoti i te x^2+(1.5x-4.25)=46

$$x ^ { 2 } + ( 1.5 x - 4.25 ) = 46$$

Whakaoti mō x

$$x = \frac{\sqrt{813} - 3}{4} \approx 6.378288715$$

$$x=\frac{-\sqrt{813}-3}{4}\approx -7.878288715$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$x^{2}+1.5x-4.25=46$$

Me tango 46 mai i ngā taha e rua o te whārite.

$$x^{2}+1.5x-4.25-46=46-46$$

Mā te tango i te 46 i a ia ake anō ka toe ko te 0.

$$x^{2}+1.5x-4.25-46=0$$

Tango 46 mai i -4.25.

$$x^{2}+1.5x-50.25=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 1.5 mō b, me -50.25 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1.5±\sqrt{1.5^{2}-4\left(-50.25\right)}}{2}$$

Pūruatia 1.5 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-1.5±\sqrt{2.25-4\left(-50.25\right)}}{2}$$

Whakareatia -4 ki te -50.25.

$$x=\frac{-1.5±\sqrt{2.25+201}}{2}$$

Tāpiri 2.25 ki te 201.

$$x=\frac{-1.5±\sqrt{203.25}}{2}$$

Tuhia te pūtakerua o te 203.25.

$$x=\frac{-1.5±\frac{\sqrt{813}}{2}}{2}$$

Nā, me whakaoti te whārite x=\frac{-1.5±\frac{\sqrt{813}}{2}}{2} ina he tāpiri te ±. Tāpiri -1.5 ki te \frac{\sqrt{813}}{2}.

$$x=\frac{\sqrt{813}-3}{2\times 2}$$

Whakawehe \frac{-3+\sqrt{813}}{2} ki te 2.

$$x=\frac{\sqrt{813}-3}{4}$$

Nā, me whakaoti te whārite x=\frac{-1.5±\frac{\sqrt{813}}{2}}{2} ina he tango te ±. Tango \frac{\sqrt{813}}{2} mai i -1.5.

$$x=\frac{-\sqrt{813}-3}{2\times 2}$$

Whakawehe \frac{-3-\sqrt{813}}{2} ki te 2.

$$x=\frac{-\sqrt{813}-3}{4}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{813}-3}{4} x=\frac{-\sqrt{813}-3}{4}$$

Ngā Upane mō te Whakaoti i te Pūrua

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.

$$x^{2}+1.5x-4.25=46$$

Me tāpiri 4.25 ki ngā taha e rua o te whārite.

$$x^{2}+1.5x-4.25-\left(-4.25\right)=46-\left(-4.25\right)$$

Mā te tango i te -4.25 i a ia ake anō ka toe ko te 0.

$$x^{2}+1.5x=46-\left(-4.25\right)$$

Tango -4.25 mai i 46.

$$x^{2}+1.5x=50.25$$

Whakawehea te 1.5, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 0.75. Nā, tāpiria te pūrua o te 0.75 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+1.5x+0.75^{2}=50.25+0.75^{2}$$

Pūruatia 0.75 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+1.5x+0.5625=50.25+0.5625$$

Tāpiri 50.25 ki te 0.5625 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.

$$x^{2}+1.5x+0.5625=50.8125$$

Tauwehea x^{2}+1.5x+0.5625. 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}.

$$\left(x+0.75\right)^{2}=50.8125$$

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

$$\sqrt{\left(x+0.75\right)^{2}}=\sqrt{50.8125}$$

Whakarūnātia.

$$x+0.75=\frac{\sqrt{813}}{4} x+0.75=-\frac{\sqrt{813}}{4}$$

Me tango 0.75 mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{813}-3}{4} x=\frac{-\sqrt{813}-3}{4}$$