Whakaoti i te 125x^2+x-12=19x

$$125 x ^ { 2 } + x - 12 = 19 x$$

Whakaoti mō x

$$x=\frac{\sqrt{1581}+9}{125}\approx 0.390094326$$

$$x=\frac{9-\sqrt{1581}}{125}\approx -0.246094326$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 19x mai i ngā taha e rua.

$$125x^{2}+x-12-19x=0$$

Pahekotia te x me -19x, ka -18x.

$$125x^{2}-18x-12=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 125 mō a, -18 mō b, me -12 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\times 125\left(-12\right)}}{2\times 125}$$

Pūrua -18.

$$x=\frac{-\left(-18\right)±\sqrt{324-4\times 125\left(-12\right)}}{2\times 125}$$

Whakareatia -4 ki te 125.

$$x=\frac{-\left(-18\right)±\sqrt{324-500\left(-12\right)}}{2\times 125}$$

Whakareatia -500 ki te -12.

$$x=\frac{-\left(-18\right)±\sqrt{324+6000}}{2\times 125}$$

Tāpiri 324 ki te 6000.

$$x=\frac{-\left(-18\right)±\sqrt{6324}}{2\times 125}$$

Tuhia te pūtakerua o te 6324.

$$x=\frac{-\left(-18\right)±2\sqrt{1581}}{2\times 125}$$

Ko te tauaro o -18 ko 18.

$$x=\frac{18±2\sqrt{1581}}{2\times 125}$$

Whakareatia 2 ki te 125.

$$x=\frac{18±2\sqrt{1581}}{250}$$

Nā, me whakaoti te whārite x=\frac{18±2\sqrt{1581}}{250} ina he tāpiri te ±. Tāpiri 18 ki te 2\sqrt{1581}.

$$x=\frac{2\sqrt{1581}+18}{250}$$

Whakawehe 18+2\sqrt{1581} ki te 250.

$$x=\frac{\sqrt{1581}+9}{125}$$

Nā, me whakaoti te whārite x=\frac{18±2\sqrt{1581}}{250} ina he tango te ±. Tango 2\sqrt{1581} mai i 18.

$$x=\frac{18-2\sqrt{1581}}{250}$$

Whakawehe 18-2\sqrt{1581} ki te 250.

$$x=\frac{9-\sqrt{1581}}{125}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{1581}+9}{125} x=\frac{9-\sqrt{1581}}{125}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 19x mai i ngā taha e rua.

$$125x^{2}+x-12-19x=0$$

Pahekotia te x me -19x, ka -18x.

$$125x^{2}-18x-12=0$$

Me tāpiri te 12 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$125x^{2}-18x=12$$

Whakawehea ngā taha e rua ki te 125.

$$\frac{125x^{2}-18x}{125}=\frac{12}{125}$$

Mā te whakawehe ki te 125 ka wetekia te whakareanga ki te 125.

$$x^{2}-\frac{18}{125}x=\frac{12}{125}$$

Whakawehea te -\frac{18}{125}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{9}{125}. Nā, tāpiria te pūrua o te -\frac{9}{125} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{18}{125}x+\left(-\frac{9}{125}\right)^{2}=\frac{12}{125}+\left(-\frac{9}{125}\right)^{2}$$

Pūruatia -\frac{9}{125} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{18}{125}x+\frac{81}{15625}=\frac{12}{125}+\frac{81}{15625}$$

Tāpiri \frac{12}{125} ki te \frac{81}{15625} 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.

$$x^{2}-\frac{18}{125}x+\frac{81}{15625}=\frac{1581}{15625}$$

Tauwehea x^{2}-\frac{18}{125}x+\frac{81}{15625}. 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}.

$$\left(x-\frac{9}{125}\right)^{2}=\frac{1581}{15625}$$

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

$$\sqrt{\left(x-\frac{9}{125}\right)^{2}}=\sqrt{\frac{1581}{15625}}$$

Whakarūnātia.

$$x-\frac{9}{125}=\frac{\sqrt{1581}}{125} x-\frac{9}{125}=-\frac{\sqrt{1581}}{125}$$

Me tāpiri \frac{9}{125} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{1581}+9}{125} x=\frac{9-\sqrt{1581}}{125}$$