Whakaoti i te (x+4)(2x-3)=6

$$( x + 4 ) ( 2 x - 3 ) = 6$$

Whakaoti mō x

$$x = -\frac{9}{2} = -4\frac{1}{2} = -4.5$$

$$x=2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$2x^{2}+5x-12=6$$

Tangohia te 6 mai i ngā taha e rua.

$$2x^{2}+5x-12-6=0$$

Tangohia te 6 i te -12, ka -18.

$$2x^{2}+5x-18=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 5 mō b, me -18 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-5±\sqrt{5^{2}-4\times 2\left(-18\right)}}{2\times 2}$$

Pūrua 5.

$$x=\frac{-5±\sqrt{25-4\times 2\left(-18\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-5±\sqrt{25-8\left(-18\right)}}{2\times 2}$$

Whakareatia -8 ki te -18.

$$x=\frac{-5±\sqrt{25+144}}{2\times 2}$$

Tāpiri 25 ki te 144.

$$x=\frac{-5±\sqrt{169}}{2\times 2}$$

Tuhia te pūtakerua o te 169.

$$x=\frac{-5±13}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-5±13}{4}$$

Nā, me whakaoti te whārite x=\frac{-5±13}{4} ina he tāpiri te ±. Tāpiri -5 ki te 13.

$$x=\frac{8}{4}$$

Whakawehe 8 ki te 4.

$$x=2$$

Nā, me whakaoti te whārite x=\frac{-5±13}{4} ina he tango te ±. Tango 13 mai i -5.

$$x=-\frac{18}{4}$$

Whakahekea te hautanga \frac{-18}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=-\frac{9}{2}$$

Kua oti te whārite te whakatau.

$$x=2 x=-\frac{9}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$2x^{2}+5x-12=6$$

Me tāpiri te 12 ki ngā taha e rua.

$$2x^{2}+5x=6+12$$

Tāpirihia te 6 ki te 12, ka 18.

$$2x^{2}+5x=18$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}+5x}{2}=\frac{18}{2}$$

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

$$x^{2}+\frac{5}{2}x=\frac{18}{2}$$

Whakawehe 18 ki te 2.

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

Whakawehea te \frac{5}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{5}{4}. Nā, tāpiria te pūrua o te \frac{5}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{5}{2}x+\left(\frac{5}{4}\right)^{2}=9+\left(\frac{5}{4}\right)^{2}$$

Pūruatia \frac{5}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{5}{2}x+\frac{25}{16}=9+\frac{25}{16}$$

Tāpiri 9 ki te \frac{25}{16}.

$$x^{2}+\frac{5}{2}x+\frac{25}{16}=\frac{169}{16}$$

Tauwehea x^{2}+\frac{5}{2}x+\frac{25}{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}.

$$\left(x+\frac{5}{4}\right)^{2}=\frac{169}{16}$$

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

$$\sqrt{\left(x+\frac{5}{4}\right)^{2}}=\sqrt{\frac{169}{16}}$$

Whakarūnātia.

$$x+\frac{5}{4}=\frac{13}{4} x+\frac{5}{4}=-\frac{13}{4}$$

Me tango \frac{5}{4} mai i ngā taha e rua o te whārite.

$$x=2 x=-\frac{9}{2}$$