Whakaoti i te (6x-3)*(5x+2)=30x

$$( 6 x - 3 ) \cdot ( 5 x + 2 ) = 30 x$$

Whakaoti mō x

$$x = \frac{\sqrt{201} + 11}{20} \approx 1.258872344$$

$$x=\frac{11-\sqrt{201}}{20}\approx -0.158872344$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 6x-3 ki te 5x+2 ka whakakotahi i ngā kupu rite.

$$30x^{2}-3x-6=30x$$

Tangohia te 30x mai i ngā taha e rua.

$$30x^{2}-3x-6-30x=0$$

Pahekotia te -3x me -30x, ka -33x.

$$30x^{2}-33x-6=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 30 mō a, -33 mō b, me -6 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-33\right)±\sqrt{\left(-33\right)^{2}-4\times 30\left(-6\right)}}{2\times 30}$$

Pūrua -33.

$$x=\frac{-\left(-33\right)±\sqrt{1089-4\times 30\left(-6\right)}}{2\times 30}$$

Whakareatia -4 ki te 30.

$$x=\frac{-\left(-33\right)±\sqrt{1089-120\left(-6\right)}}{2\times 30}$$

Whakareatia -120 ki te -6.

$$x=\frac{-\left(-33\right)±\sqrt{1089+720}}{2\times 30}$$

Tāpiri 1089 ki te 720.

$$x=\frac{-\left(-33\right)±\sqrt{1809}}{2\times 30}$$

Tuhia te pūtakerua o te 1809.

$$x=\frac{-\left(-33\right)±3\sqrt{201}}{2\times 30}$$

Ko te tauaro o -33 ko 33.

$$x=\frac{33±3\sqrt{201}}{2\times 30}$$

Whakareatia 2 ki te 30.

$$x=\frac{33±3\sqrt{201}}{60}$$

Nā, me whakaoti te whārite x=\frac{33±3\sqrt{201}}{60} ina he tāpiri te ±. Tāpiri 33 ki te 3\sqrt{201}.

$$x=\frac{3\sqrt{201}+33}{60}$$

Whakawehe 33+3\sqrt{201} ki te 60.

$$x=\frac{\sqrt{201}+11}{20}$$

Nā, me whakaoti te whārite x=\frac{33±3\sqrt{201}}{60} ina he tango te ±. Tango 3\sqrt{201} mai i 33.

$$x=\frac{33-3\sqrt{201}}{60}$$

Whakawehe 33-3\sqrt{201} ki te 60.

$$x=\frac{11-\sqrt{201}}{20}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{201}+11}{20} x=\frac{11-\sqrt{201}}{20}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 6x-3 ki te 5x+2 ka whakakotahi i ngā kupu rite.

$$30x^{2}-3x-6=30x$$

Tangohia te 30x mai i ngā taha e rua.

$$30x^{2}-3x-6-30x=0$$

Pahekotia te -3x me -30x, ka -33x.

$$30x^{2}-33x-6=0$$

Me tāpiri te 6 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$30x^{2}-33x=6$$

Whakawehea ngā taha e rua ki te 30.

$$\frac{30x^{2}-33x}{30}=\frac{6}{30}$$

Mā te whakawehe ki te 30 ka wetekia te whakareanga ki te 30.

$$x^{2}+\left(-\frac{33}{30}\right)x=\frac{6}{30}$$

Whakahekea te hautanga \frac{-33}{30} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$x^{2}-\frac{11}{10}x=\frac{6}{30}$$

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

$$x^{2}-\frac{11}{10}x=\frac{1}{5}$$

Whakawehea te -\frac{11}{10}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{11}{20}. Nā, tāpiria te pūrua o te -\frac{11}{20} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{11}{10}x+\left(-\frac{11}{20}\right)^{2}=\frac{1}{5}+\left(-\frac{11}{20}\right)^{2}$$

Pūruatia -\frac{11}{20} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{11}{10}x+\frac{121}{400}=\frac{1}{5}+\frac{121}{400}$$

Tāpiri \frac{1}{5} ki te \frac{121}{400} 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.

$$x^{2}-\frac{11}{10}x+\frac{121}{400}=\frac{201}{400}$$

Tauwehea x^{2}-\frac{11}{10}x+\frac{121}{400}. 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}.

$$\left(x-\frac{11}{20}\right)^{2}=\frac{201}{400}$$

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

$$\sqrt{\left(x-\frac{11}{20}\right)^{2}}=\sqrt{\frac{201}{400}}$$

Whakarūnātia.

$$x-\frac{11}{20}=\frac{\sqrt{201}}{20} x-\frac{11}{20}=-\frac{\sqrt{201}}{20}$$

Me tāpiri \frac{11}{20} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{201}+11}{20} x=\frac{11-\sqrt{201}}{20}$$