Whakaoti i te -5x^2+4x=0.35

$$- 5 x ^ { 2 } + 4 x = 0.35$$

Whakaoti mō x

$$x=0.1$$

$$x=0.7$$

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.

$$-5x^{2}+4x=0.35$$

Me tango 0.35 mai i ngā taha e rua o te whārite.

$$-5x^{2}+4x-0.35=0.35-0.35$$

Mā te tango i te 0.35 i a ia ake anō ka toe ko te 0.

$$-5x^{2}+4x-0.35=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -5 mō a, 4 mō b, me -0.35 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-4±\sqrt{4^{2}-4\left(-5\right)\left(-0.35\right)}}{2\left(-5\right)}$$

Pūrua 4.

$$x=\frac{-4±\sqrt{16-4\left(-5\right)\left(-0.35\right)}}{2\left(-5\right)}$$

Whakareatia -4 ki te -5.

$$x=\frac{-4±\sqrt{16+20\left(-0.35\right)}}{2\left(-5\right)}$$

Whakareatia 20 ki te -0.35.

$$x=\frac{-4±\sqrt{16-7}}{2\left(-5\right)}$$

Tāpiri 16 ki te -7.

$$x=\frac{-4±\sqrt{9}}{2\left(-5\right)}$$

Tuhia te pūtakerua o te 9.

$$x=\frac{-4±3}{2\left(-5\right)}$$

Whakareatia 2 ki te -5.

$$x=\frac{-4±3}{-10}$$

Nā, me whakaoti te whārite x=\frac{-4±3}{-10} ina he tāpiri te ±. Tāpiri -4 ki te 3.

$$x=-\frac{1}{-10}$$

Whakawehe -1 ki te -10.

$$x=\frac{1}{10}$$

Nā, me whakaoti te whārite x=\frac{-4±3}{-10} ina he tango te ±. Tango 3 mai i -4.

$$x=-\frac{7}{-10}$$

Whakawehe -7 ki te -10.

$$x=\frac{7}{10}$$

Kua oti te whārite te whakatau.

$$x=\frac{1}{10} x=\frac{7}{10}$$

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.

$$-5x^{2}+4x=0.35$$

Whakawehea ngā taha e rua ki te -5.

$$\frac{-5x^{2}+4x}{-5}=\frac{0.35}{-5}$$

Mā te whakawehe ki te -5 ka wetekia te whakareanga ki te -5.

$$x^{2}+\frac{4}{-5}x=\frac{0.35}{-5}$$

Whakawehe 4 ki te -5.

$$x^{2}-\frac{4}{5}x=\frac{0.35}{-5}$$

Whakawehe 0.35 ki te -5.

$$x^{2}-\frac{4}{5}x=-0.07$$

Whakawehea te -\frac{4}{5}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{2}{5}. Nā, tāpiria te pūrua o te -\frac{2}{5} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{4}{5}x+\left(-\frac{2}{5}\right)^{2}=-0.07+\left(-\frac{2}{5}\right)^{2}$$

Pūruatia -\frac{2}{5} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{4}{5}x+\frac{4}{25}=-0.07+\frac{4}{25}$$

Tāpiri -0.07 ki te \frac{4}{25} 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.

$$x^{2}-\frac{4}{5}x+\frac{4}{25}=\frac{9}{100}$$

Tauwehea x^{2}-\frac{4}{5}x+\frac{4}{25}. 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}.

$$\left(x-\frac{2}{5}\right)^{2}=\frac{9}{100}$$

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

$$\sqrt{\left(x-\frac{2}{5}\right)^{2}}=\sqrt{\frac{9}{100}}$$

Whakarūnātia.

$$x-\frac{2}{5}=\frac{3}{10} x-\frac{2}{5}=-\frac{3}{10}$$

Me tāpiri \frac{2}{5} ki ngā taha e rua o te whārite.

$$x=\frac{7}{10} x=\frac{1}{10}$$