Whakaoti i te (3x-2)(2x-3)=(2x+5)(2x-1)

$$( 3 x - 2 ) ( 2 x - 3 ) = ( 2 x + 5 ) ( 2 x - 1 )$$

Whakaoti mō x

$$x = \frac{\sqrt{353} + 21}{4} \approx 9.947073557$$

$$x=\frac{21-\sqrt{353}}{4}\approx 0.552926443$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$6x^{2}-13x+6=\left(2x+5\right)\left(2x-1\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 2x+5 ki te 2x-1 ka whakakotahi i ngā kupu rite.

$$6x^{2}-13x+6=4x^{2}+8x-5$$

Tangohia te 4x^{2} mai i ngā taha e rua.

$$6x^{2}-13x+6-4x^{2}=8x-5$$

Pahekotia te 6x^{2} me -4x^{2}, ka 2x^{2}.

$$2x^{2}-13x+6=8x-5$$

Tangohia te 8x mai i ngā taha e rua.

$$2x^{2}-13x+6-8x=-5$$

Pahekotia te -13x me -8x, ka -21x.

$$2x^{2}-21x+6=-5$$

Me tāpiri te 5 ki ngā taha e rua.

$$2x^{2}-21x+6+5=0$$

Tāpirihia te 6 ki te 5, ka 11.

$$2x^{2}-21x+11=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, -21 mō b, me 11 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-21\right)±\sqrt{\left(-21\right)^{2}-4\times 2\times 11}}{2\times 2}$$

Pūrua -21.

$$x=\frac{-\left(-21\right)±\sqrt{441-4\times 2\times 11}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-\left(-21\right)±\sqrt{441-8\times 11}}{2\times 2}$$

Whakareatia -8 ki te 11.

$$x=\frac{-\left(-21\right)±\sqrt{441-88}}{2\times 2}$$

Tāpiri 441 ki te -88.

$$x=\frac{-\left(-21\right)±\sqrt{353}}{2\times 2}$$

Ko te tauaro o -21 ko 21.

$$x=\frac{21±\sqrt{353}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{21±\sqrt{353}}{4}$$

Nā, me whakaoti te whārite x=\frac{21±\sqrt{353}}{4} ina he tāpiri te ±. Tāpiri 21 ki te \sqrt{353}.

$$x=\frac{\sqrt{353}+21}{4}$$

Nā, me whakaoti te whārite x=\frac{21±\sqrt{353}}{4} ina he tango te ±. Tango \sqrt{353} mai i 21.

$$x=\frac{21-\sqrt{353}}{4}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{353}+21}{4} x=\frac{21-\sqrt{353}}{4}$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$6x^{2}-13x+6=\left(2x+5\right)\left(2x-1\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 2x+5 ki te 2x-1 ka whakakotahi i ngā kupu rite.

$$6x^{2}-13x+6=4x^{2}+8x-5$$

Tangohia te 4x^{2} mai i ngā taha e rua.

$$6x^{2}-13x+6-4x^{2}=8x-5$$

Pahekotia te 6x^{2} me -4x^{2}, ka 2x^{2}.

$$2x^{2}-13x+6=8x-5$$

Tangohia te 8x mai i ngā taha e rua.

$$2x^{2}-13x+6-8x=-5$$

Pahekotia te -13x me -8x, ka -21x.

$$2x^{2}-21x+6=-5$$

Tangohia te 6 mai i ngā taha e rua.

$$2x^{2}-21x=-5-6$$

Tangohia te 6 i te -5, ka -11.

$$2x^{2}-21x=-11$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}-21x}{2}=-\frac{11}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$x^{2}-\frac{21}{2}x=-\frac{11}{2}$$

Whakawehea te -\frac{21}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{21}{4}. Nā, tāpiria te pūrua o te -\frac{21}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{21}{2}x+\left(-\frac{21}{4}\right)^{2}=-\frac{11}{2}+\left(-\frac{21}{4}\right)^{2}$$

Pūruatia -\frac{21}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{21}{2}x+\frac{441}{16}=-\frac{11}{2}+\frac{441}{16}$$

Tāpiri -\frac{11}{2} ki te \frac{441}{16} 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.

$$x^{2}-\frac{21}{2}x+\frac{441}{16}=\frac{353}{16}$$

Tauwehea x^{2}-\frac{21}{2}x+\frac{441}{16}. 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}.

$$\left(x-\frac{21}{4}\right)^{2}=\frac{353}{16}$$

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

$$\sqrt{\left(x-\frac{21}{4}\right)^{2}}=\sqrt{\frac{353}{16}}$$

Whakarūnātia.

$$x-\frac{21}{4}=\frac{\sqrt{353}}{4} x-\frac{21}{4}=-\frac{\sqrt{353}}{4}$$

Me tāpiri \frac{21}{4} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{353}+21}{4} x=\frac{21-\sqrt{353}}{4}$$