Whakaoti i te 2x(x+1)=3(4-x)

$$2 x ( x + 1 ) = 3 ( 4 - x )$$

Whakaoti mō x

$$x=-4$$

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te x+1.

$$2x^{2}+2x=3\left(4-x\right)$$

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

$$2x^{2}+2x=12-3x$$

Tangohia te 12 mai i ngā taha e rua.

$$2x^{2}+2x-12=-3x$$

Me tāpiri te 3x ki ngā taha e rua.

$$2x^{2}+2x-12+3x=0$$

Pahekotia te 2x me 3x, ka 5x.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 5 mō b, me -12 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-5±\sqrt{5^{2}-4\times 2\left(-12\right)}}{2\times 2}$$

Pūrua 5.

$$x=\frac{-5±\sqrt{25-4\times 2\left(-12\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-5±\sqrt{25-8\left(-12\right)}}{2\times 2}$$

Whakareatia -8 ki te -12.

$$x=\frac{-5±\sqrt{25+96}}{2\times 2}$$

Tāpiri 25 ki te 96.

$$x=\frac{-5±\sqrt{121}}{2\times 2}$$

Tuhia te pūtakerua o te 121.

$$x=\frac{-5±11}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-5±11}{4}$$

Nā, me whakaoti te whārite x=\frac{-5±11}{4} ina he tāpiri te ±. Tāpiri -5 ki te 11.

$$x=\frac{6}{4}$$

Whakahekea te hautanga \frac{6}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{3}{2}$$

Nā, me whakaoti te whārite x=\frac{-5±11}{4} ina he tango te ±. Tango 11 mai i -5.

$$x=-\frac{16}{4}$$

Whakawehe -16 ki te 4.

$$x=-4$$

Kua oti te whārite te whakatau.

$$x=\frac{3}{2} x=-4$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te x+1.

$$2x^{2}+2x=3\left(4-x\right)$$

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

$$2x^{2}+2x=12-3x$$

Me tāpiri te 3x ki ngā taha e rua.

$$2x^{2}+2x+3x=12$$

Pahekotia te 2x me 3x, ka 5x.

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

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}+5x}{2}=\frac{12}{2}$$

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

$$x^{2}+\frac{5}{2}x=\frac{12}{2}$$

Whakawehe 12 ki te 2.

$$x^{2}+\frac{5}{2}x=6$$

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.

$$x^{2}+\frac{5}{2}x+\left(\frac{5}{4}\right)^{2}=6+\left(\frac{5}{4}\right)^{2}$$

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

$$x^{2}+\frac{5}{2}x+\frac{25}{16}=6+\frac{25}{16}$$

Tāpiri 6 ki te \frac{25}{16}.

$$x^{2}+\frac{5}{2}x+\frac{25}{16}=\frac{121}{16}$$

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}.

$$\left(x+\frac{5}{4}\right)^{2}=\frac{121}{16}$$

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

$$\sqrt{\left(x+\frac{5}{4}\right)^{2}}=\sqrt{\frac{121}{16}}$$

Whakarūnātia.

$$x+\frac{5}{4}=\frac{11}{4} x+\frac{5}{4}=-\frac{11}{4}$$

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

$$x=\frac{3}{2} x=-4$$