Whakaoti i te (384x-048)*(3x+4)=30

$$(384x-048) \times (3x+4)=30$$

Whakaoti mō x

$$x=\frac{\sqrt{271}}{24}-\frac{2}{3}\approx 0.019253235$$

$$x=-\frac{\sqrt{271}}{24}-\frac{2}{3}\approx -1.352586568$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 0 ki te 48, ka 0.

$$\left(384x-0\right)\left(3x+4\right)=30$$

Whakamahia te āhuatanga tohatoha hei whakarea te 384x-0 ki te 3x+4.

$$3\left(384x-0\right)x+4\left(384x-0\right)=30$$

Tangohia te 30 mai i ngā taha e rua.

$$3\left(384x-0\right)x+4\left(384x-0\right)-30=0$$

Whakaraupapatia anō ngā kīanga tau.

$$3\times 384xx+4\times 384x-30=0$$

Whakareatia te x ki te x, ka x^{2}.

$$3\times 384x^{2}+4\times 384x-30=0$$

Whakareatia te 3 ki te 384, ka 1152. Whakareatia te 4 ki te 384, ka 1536.

$$1152x^{2}+1536x-30=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1152 mō a, 1536 mō b, me -30 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1536±\sqrt{1536^{2}-4\times 1152\left(-30\right)}}{2\times 1152}$$

Pūrua 1536.

$$x=\frac{-1536±\sqrt{2359296-4\times 1152\left(-30\right)}}{2\times 1152}$$

Whakareatia -4 ki te 1152.

$$x=\frac{-1536±\sqrt{2359296-4608\left(-30\right)}}{2\times 1152}$$

Whakareatia -4608 ki te -30.

$$x=\frac{-1536±\sqrt{2359296+138240}}{2\times 1152}$$

Tāpiri 2359296 ki te 138240.

$$x=\frac{-1536±\sqrt{2497536}}{2\times 1152}$$

Tuhia te pūtakerua o te 2497536.

$$x=\frac{-1536±96\sqrt{271}}{2\times 1152}$$

Whakareatia 2 ki te 1152.

$$x=\frac{-1536±96\sqrt{271}}{2304}$$

Nā, me whakaoti te whārite x=\frac{-1536±96\sqrt{271}}{2304} ina he tāpiri te ±. Tāpiri -1536 ki te 96\sqrt{271}.

$$x=\frac{96\sqrt{271}-1536}{2304}$$

Whakawehe -1536+96\sqrt{271} ki te 2304.

$$x=\frac{\sqrt{271}}{24}-\frac{2}{3}$$

Nā, me whakaoti te whārite x=\frac{-1536±96\sqrt{271}}{2304} ina he tango te ±. Tango 96\sqrt{271} mai i -1536.

$$x=\frac{-96\sqrt{271}-1536}{2304}$$

Whakawehe -1536-96\sqrt{271} ki te 2304.

$$x=-\frac{\sqrt{271}}{24}-\frac{2}{3}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{271}}{24}-\frac{2}{3} x=-\frac{\sqrt{271}}{24}-\frac{2}{3}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te 0 ki te 48, ka 0.

$$\left(384x-0\right)\left(3x+4\right)=30$$

Whakamahia te āhuatanga tohatoha hei whakarea te 384x-0 ki te 3x+4.

$$3\left(384x-0\right)x+4\left(384x-0\right)=30$$

Whakaraupapatia anō ngā kīanga tau.

$$3\times 384xx+4\times 384x=30$$

Whakareatia te x ki te x, ka x^{2}.

$$3\times 384x^{2}+4\times 384x=30$$

Whakareatia te 3 ki te 384, ka 1152. Whakareatia te 4 ki te 384, ka 1536.

$$1152x^{2}+1536x=30$$

Whakawehea ngā taha e rua ki te 1152.

$$\frac{1152x^{2}+1536x}{1152}=\frac{30}{1152}$$

Mā te whakawehe ki te 1152 ka wetekia te whakareanga ki te 1152.

$$x^{2}+\frac{1536}{1152}x=\frac{30}{1152}$$

Whakahekea te hautanga \frac{1536}{1152} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 384.

$$x^{2}+\frac{4}{3}x=\frac{30}{1152}$$

Whakahekea te hautanga \frac{30}{1152} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$x^{2}+\frac{4}{3}x=\frac{5}{192}$$

Whakawehea te \frac{4}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{2}{3}. Nā, tāpiria te pūrua o te \frac{2}{3} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{4}{3}x+\left(\frac{2}{3}\right)^{2}=\frac{5}{192}+\left(\frac{2}{3}\right)^{2}$$

Pūruatia \frac{2}{3} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{4}{3}x+\frac{4}{9}=\frac{5}{192}+\frac{4}{9}$$

Tāpiri \frac{5}{192} ki te \frac{4}{9} 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.

$$x^{2}+\frac{4}{3}x+\frac{4}{9}=\frac{271}{576}$$

Tauwehea x^{2}+\frac{4}{3}x+\frac{4}{9}. 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}.

$$\left(x+\frac{2}{3}\right)^{2}=\frac{271}{576}$$

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

$$\sqrt{\left(x+\frac{2}{3}\right)^{2}}=\sqrt{\frac{271}{576}}$$

Whakarūnātia.

$$x+\frac{2}{3}=\frac{\sqrt{271}}{24} x+\frac{2}{3}=-\frac{\sqrt{271}}{24}$$

Me tango \frac{2}{3} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{271}}{24}-\frac{2}{3} x=-\frac{\sqrt{271}}{24}-\frac{2}{3}$$