Whakaoti i te (3x+2)(3x-4)=7

$$(3x+2)(3x-4)=7$$

Whakaoti mō x

$$x=-1$$

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 3x+2 ki te 3x-4 ka whakakotahi i ngā kupu rite.

$$9x^{2}-6x-8=7$$

Tangohia te 7 mai i ngā taha e rua.

$$9x^{2}-6x-8-7=0$$

Tangohia te 7 i te -8, ka -15.

$$9x^{2}-6x-15=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 9 mō a, -6 mō b, me -15 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 9\left(-15\right)}}{2\times 9}$$

Pūrua -6.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\times 9\left(-15\right)}}{2\times 9}$$

Whakareatia -4 ki te 9.

$$x=\frac{-\left(-6\right)±\sqrt{36-36\left(-15\right)}}{2\times 9}$$

Whakareatia -36 ki te -15.

$$x=\frac{-\left(-6\right)±\sqrt{36+540}}{2\times 9}$$

Tāpiri 36 ki te 540.

$$x=\frac{-\left(-6\right)±\sqrt{576}}{2\times 9}$$

Tuhia te pūtakerua o te 576.

$$x=\frac{-\left(-6\right)±24}{2\times 9}$$

Ko te tauaro o -6 ko 6.

$$x=\frac{6±24}{2\times 9}$$

Whakareatia 2 ki te 9.

$$x=\frac{6±24}{18}$$

Nā, me whakaoti te whārite x=\frac{6±24}{18} ina he tāpiri te ±. Tāpiri 6 ki te 24.

$$x=\frac{30}{18}$$

Whakahekea te hautanga \frac{30}{18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$x=\frac{5}{3}$$

Nā, me whakaoti te whārite x=\frac{6±24}{18} ina he tango te ±. Tango 24 mai i 6.

$$x=-\frac{18}{18}$$

Whakawehe -18 ki te 18.

$$x=-1$$

Kua oti te whārite te whakatau.

$$x=\frac{5}{3} x=-1$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 3x+2 ki te 3x-4 ka whakakotahi i ngā kupu rite.

$$9x^{2}-6x-8=7$$

Me tāpiri te 8 ki ngā taha e rua.

$$9x^{2}-6x=7+8$$

Tāpirihia te 7 ki te 8, ka 15.

$$9x^{2}-6x=15$$

Whakawehea ngā taha e rua ki te 9.

$$\frac{9x^{2}-6x}{9}=\frac{15}{9}$$

Mā te whakawehe ki te 9 ka wetekia te whakareanga ki te 9.

$$x^{2}+\left(-\frac{6}{9}\right)x=\frac{15}{9}$$

Whakahekea te hautanga \frac{-6}{9} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$x^{2}-\frac{2}{3}x=\frac{15}{9}$$

Whakahekea te hautanga \frac{15}{9} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

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

Whakawehea te -\frac{2}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{3}. Nā, tāpiria te pūrua o te -\frac{1}{3} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{2}{3}x+\left(-\frac{1}{3}\right)^{2}=\frac{5}{3}+\left(-\frac{1}{3}\right)^{2}$$

Pūruatia -\frac{1}{3} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{2}{3}x+\frac{1}{9}=\frac{5}{3}+\frac{1}{9}$$

Tāpiri \frac{5}{3} ki te \frac{1}{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.

$$x^{2}-\frac{2}{3}x+\frac{1}{9}=\frac{16}{9}$$

Tauwehea x^{2}-\frac{2}{3}x+\frac{1}{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}.

$$\left(x-\frac{1}{3}\right)^{2}=\frac{16}{9}$$

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

$$\sqrt{\left(x-\frac{1}{3}\right)^{2}}=\sqrt{\frac{16}{9}}$$

Whakarūnātia.

$$x-\frac{1}{3}=\frac{4}{3} x-\frac{1}{3}=-\frac{4}{3}$$

Me tāpiri \frac{1}{3} ki ngā taha e rua o te whārite.

$$x=\frac{5}{3} x=-1$$