Whakaoti i te (7-2x)(x-2)=1.12

$$(7-2x)(x-2)=1.12$$

Whakaoti mō x

$$x=2.8$$

$$x=2.7$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 7-2x ki te x-2 ka whakakotahi i ngā kupu rite.

$$11x-14-2x^{2}=1.12$$

Tangohia te 1.12 mai i ngā taha e rua.

$$11x-14-2x^{2}-1.12=0$$

Tangohia te 1.12 i te -14, ka -15.12.

$$11x-15.12-2x^{2}=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$-2x^{2}+11x-15.12=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -2 mō a, 11 mō b, me -15.12 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-11±\sqrt{11^{2}-4\left(-2\right)\left(-15.12\right)}}{2\left(-2\right)}$$

Pūrua 11.

$$x=\frac{-11±\sqrt{121-4\left(-2\right)\left(-15.12\right)}}{2\left(-2\right)}$$

Whakareatia -4 ki te -2.

$$x=\frac{-11±\sqrt{121+8\left(-15.12\right)}}{2\left(-2\right)}$$

Whakareatia 8 ki te -15.12.

$$x=\frac{-11±\sqrt{121-120.96}}{2\left(-2\right)}$$

Tāpiri 121 ki te -120.96.

$$x=\frac{-11±\sqrt{0.04}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te 0.04.

$$x=\frac{-11±\frac{1}{5}}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=\frac{-11±\frac{1}{5}}{-4}$$

Nā, me whakaoti te whārite x=\frac{-11±\frac{1}{5}}{-4} ina he tāpiri te ±. Tāpiri -11 ki te \frac{1}{5}.

$$x=-\frac{\frac{54}{5}}{-4}$$

Whakawehe -\frac{54}{5} ki te -4.

$$x=\frac{27}{10}$$

Nā, me whakaoti te whārite x=\frac{-11±\frac{1}{5}}{-4} ina he tango te ±. Tango \frac{1}{5} mai i -11.

$$x=-\frac{\frac{56}{5}}{-4}$$

Whakawehe -\frac{56}{5} ki te -4.

$$x=\frac{14}{5}$$

Kua oti te whārite te whakatau.

$$x=\frac{27}{10} x=\frac{14}{5}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 7-2x ki te x-2 ka whakakotahi i ngā kupu rite.

$$11x-14-2x^{2}=1.12$$

Me tāpiri te 14 ki ngā taha e rua.

$$11x-2x^{2}=1.12+14$$

Tāpirihia te 1.12 ki te 14, ka 15.12.

$$11x-2x^{2}=15.12$$

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$-2x^{2}+11x=15.12$$

Whakawehea ngā taha e rua ki te -2.

$$\frac{-2x^{2}+11x}{-2}=\frac{15.12}{-2}$$

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

$$x^{2}+\frac{11}{-2}x=\frac{15.12}{-2}$$

Whakawehe 11 ki te -2.

$$x^{2}-\frac{11}{2}x=\frac{15.12}{-2}$$

Whakawehe 15.12 ki te -2.

$$x^{2}-\frac{11}{2}x=-7.56$$

Whakawehea te -\frac{11}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{11}{4}. Nā, tāpiria te pūrua o te -\frac{11}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{11}{2}x+\left(-\frac{11}{4}\right)^{2}=-7.56+\left(-\frac{11}{4}\right)^{2}$$

Pūruatia -\frac{11}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{11}{2}x+\frac{121}{16}=-7.56+\frac{121}{16}$$

Tāpiri -7.56 ki te \frac{121}{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.

$$x^{2}-\frac{11}{2}x+\frac{121}{16}=\frac{1}{400}$$

Tauwehea x^{2}-\frac{11}{2}x+\frac{121}{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}.

$$\left(x-\frac{11}{4}\right)^{2}=\frac{1}{400}$$

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

$$\sqrt{\left(x-\frac{11}{4}\right)^{2}}=\sqrt{\frac{1}{400}}$$

Whakarūnātia.

$$x-\frac{11}{4}=\frac{1}{20} x-\frac{11}{4}=-\frac{1}{20}$$

Me tāpiri \frac{11}{4} ki ngā taha e rua o te whārite.

$$x=\frac{14}{5} x=\frac{27}{10}$$