Whakaoti i te x^2+0.4x-7.48=0

$$x ^ { 2 } + 0.4 x - 7.48 = 0$$

Whakaoti mō x

$$x = \frac{2 \sqrt{47} - 1}{5} \approx 2.54226184$$

$$x=\frac{-2\sqrt{47}-1}{5}\approx -2.94226184$$

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.

$$x^{2}+0.4x-7.48=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0.4 mō b, me -7.48 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-0.4±\sqrt{0.4^{2}-4\left(-7.48\right)}}{2}$$

Pūruatia 0.4 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-0.4±\sqrt{0.16-4\left(-7.48\right)}}{2}$$

Whakareatia -4 ki te -7.48.

$$x=\frac{-0.4±\sqrt{\frac{4+748}{25}}}{2}$$

Tāpiri 0.16 ki te 29.92 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.

$$x=\frac{-0.4±\sqrt{30.08}}{2}$$

Tuhia te pūtakerua o te 30.08.

$$x=\frac{-0.4±\frac{4\sqrt{47}}{5}}{2}$$

Nā, me whakaoti te whārite x=\frac{-0.4±\frac{4\sqrt{47}}{5}}{2} ina he tāpiri te ±. Tāpiri -0.4 ki te \frac{4\sqrt{47}}{5}.

$$x=\frac{4\sqrt{47}-2}{2\times 5}$$

Whakawehe \frac{-2+4\sqrt{47}}{5} ki te 2.

$$x=\frac{2\sqrt{47}-1}{5}$$

Nā, me whakaoti te whārite x=\frac{-0.4±\frac{4\sqrt{47}}{5}}{2} ina he tango te ±. Tango \frac{4\sqrt{47}}{5} mai i -0.4.

$$x=\frac{-4\sqrt{47}-2}{2\times 5}$$

Whakawehe \frac{-2-4\sqrt{47}}{5} ki te 2.

$$x=\frac{-2\sqrt{47}-1}{5}$$

Kua oti te whārite te whakatau.

$$x=\frac{2\sqrt{47}-1}{5} x=\frac{-2\sqrt{47}-1}{5}$$

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.

$$x^{2}+0.4x-7.48=0$$

Me tāpiri 7.48 ki ngā taha e rua o te whārite.

$$x^{2}+0.4x-7.48-\left(-7.48\right)=-\left(-7.48\right)$$

Mā te tango i te -7.48 i a ia ake anō ka toe ko te 0.

$$x^{2}+0.4x=-\left(-7.48\right)$$

Tango -7.48 mai i 0.

$$x^{2}+0.4x=7.48$$

Whakawehea te 0.4, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 0.2. Nā, tāpiria te pūrua o te 0.2 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+0.4x+0.2^{2}=7.48+0.2^{2}$$

Pūruatia 0.2 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+0.4x+0.04=\frac{187+1}{25}$$

Tāpiri 7.48 ki te 0.04 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.

$$x^{2}+0.4x+0.04=7.52$$

Tauwehea x^{2}+0.4x+0.04. 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}.

$$\left(x+0.2\right)^{2}=7.52$$

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

$$\sqrt{\left(x+0.2\right)^{2}}=\sqrt{7.52}$$

Whakarūnātia.

$$x+0.2=\frac{2\sqrt{47}}{5} x+0.2=-\frac{2\sqrt{47}}{5}$$

Me tango 0.2 mai i ngā taha e rua o te whārite.

$$x=\frac{2\sqrt{47}-1}{5} x=\frac{-2\sqrt{47}-1}{5}$$