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

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

Whakaoti mō x

$$x=3$$

$$x = \frac{7}{4} = 1\frac{3}{4} = 1.75$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$-4x^{2}+18x-18=-x+3$$

Me tāpiri te x ki ngā taha e rua.

$$-4x^{2}+18x-18+x=3$$

Pahekotia te 18x me x, ka 19x.

$$-4x^{2}+19x-18=3$$

Tangohia te 3 mai i ngā taha e rua.

$$-4x^{2}+19x-18-3=0$$

Tangohia te 3 i te -18, ka -21.

$$-4x^{2}+19x-21=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -4 mō a, 19 mō b, me -21 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-19±\sqrt{19^{2}-4\left(-4\right)\left(-21\right)}}{2\left(-4\right)}$$

Pūrua 19.

$$x=\frac{-19±\sqrt{361-4\left(-4\right)\left(-21\right)}}{2\left(-4\right)}$$

Whakareatia -4 ki te -4.

$$x=\frac{-19±\sqrt{361+16\left(-21\right)}}{2\left(-4\right)}$$

Whakareatia 16 ki te -21.

$$x=\frac{-19±\sqrt{361-336}}{2\left(-4\right)}$$

Tāpiri 361 ki te -336.

$$x=\frac{-19±\sqrt{25}}{2\left(-4\right)}$$

Tuhia te pūtakerua o te 25.

$$x=\frac{-19±5}{2\left(-4\right)}$$

Whakareatia 2 ki te -4.

$$x=\frac{-19±5}{-8}$$

Nā, me whakaoti te whārite x=\frac{-19±5}{-8} ina he tāpiri te ±. Tāpiri -19 ki te 5.

$$x=-\frac{14}{-8}$$

Whakahekea te hautanga \frac{-14}{-8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{7}{4}$$

Nā, me whakaoti te whārite x=\frac{-19±5}{-8} ina he tango te ±. Tango 5 mai i -19.

$$x=-\frac{24}{-8}$$

Whakawehe -24 ki te -8.

$$x=3$$

Kua oti te whārite te whakatau.

$$x=\frac{7}{4} x=3$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$-4x^{2}+18x-18=-x+3$$

Me tāpiri te x ki ngā taha e rua.

$$-4x^{2}+18x-18+x=3$$

Pahekotia te 18x me x, ka 19x.

$$-4x^{2}+19x-18=3$$

Me tāpiri te 18 ki ngā taha e rua.

$$-4x^{2}+19x=3+18$$

Tāpirihia te 3 ki te 18, ka 21.

$$-4x^{2}+19x=21$$

Whakawehea ngā taha e rua ki te -4.

$$\frac{-4x^{2}+19x}{-4}=\frac{21}{-4}$$

Mā te whakawehe ki te -4 ka wetekia te whakareanga ki te -4.

$$x^{2}+\frac{19}{-4}x=\frac{21}{-4}$$

Whakawehe 19 ki te -4.

$$x^{2}-\frac{19}{4}x=\frac{21}{-4}$$

Whakawehe 21 ki te -4.

$$x^{2}-\frac{19}{4}x=-\frac{21}{4}$$

Whakawehea te -\frac{19}{4}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{19}{8}. Nā, tāpiria te pūrua o te -\frac{19}{8} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{19}{4}x+\left(-\frac{19}{8}\right)^{2}=-\frac{21}{4}+\left(-\frac{19}{8}\right)^{2}$$

Pūruatia -\frac{19}{8} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{19}{4}x+\frac{361}{64}=-\frac{21}{4}+\frac{361}{64}$$

Tāpiri -\frac{21}{4} ki te \frac{361}{64} 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.

$$x^{2}-\frac{19}{4}x+\frac{361}{64}=\frac{25}{64}$$

Tauwehea x^{2}-\frac{19}{4}x+\frac{361}{64}. 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}.

$$\left(x-\frac{19}{8}\right)^{2}=\frac{25}{64}$$

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

$$\sqrt{\left(x-\frac{19}{8}\right)^{2}}=\sqrt{\frac{25}{64}}$$

Whakarūnātia.

$$x-\frac{19}{8}=\frac{5}{8} x-\frac{19}{8}=-\frac{5}{8}$$

Me tāpiri \frac{19}{8} ki ngā taha e rua o te whārite.

$$x=3 x=\frac{7}{4}$$