Whakaoti i te 9-3x/9=15-9x/9x

$$\frac{ 9-3x }{ 9 } = \frac{ 15-9x }{ 9x }$$

Whakaoti mō x

$$x=1$$

$$x=5$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 9x, arā, te tauraro pātahi he tino iti rawa te kitea o 9,9x.

$$x\left(9-3x\right)=15-9x$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 9-3x.

$$9x-3x^{2}=15-9x$$

Tangohia te 15 mai i ngā taha e rua.

$$9x-3x^{2}-15=-9x$$

Me tāpiri te 9x ki ngā taha e rua.

$$9x-3x^{2}-15+9x=0$$

Pahekotia te 9x me 9x, ka 18x.

$$18x-3x^{2}-15=0$$

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.

$$-3x^{2}+18x-15=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -3 mō a, 18 mō b, me -15 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-18±\sqrt{18^{2}-4\left(-3\right)\left(-15\right)}}{2\left(-3\right)}$$

Pūrua 18.

$$x=\frac{-18±\sqrt{324-4\left(-3\right)\left(-15\right)}}{2\left(-3\right)}$$

Whakareatia -4 ki te -3.

$$x=\frac{-18±\sqrt{324+12\left(-15\right)}}{2\left(-3\right)}$$

Whakareatia 12 ki te -15.

$$x=\frac{-18±\sqrt{324-180}}{2\left(-3\right)}$$

Tāpiri 324 ki te -180.

$$x=\frac{-18±\sqrt{144}}{2\left(-3\right)}$$

Tuhia te pūtakerua o te 144.

$$x=\frac{-18±12}{2\left(-3\right)}$$

Whakareatia 2 ki te -3.

$$x=\frac{-18±12}{-6}$$

Nā, me whakaoti te whārite x=\frac{-18±12}{-6} ina he tāpiri te ±. Tāpiri -18 ki te 12.

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

Whakawehe -6 ki te -6.

$$x=1$$

Nā, me whakaoti te whārite x=\frac{-18±12}{-6} ina he tango te ±. Tango 12 mai i -18.

$$x=-\frac{30}{-6}$$

Whakawehe -30 ki te -6.

$$x=5$$

Kua oti te whārite te whakatau.

$$x=1 x=5$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 9x, arā, te tauraro pātahi he tino iti rawa te kitea o 9,9x.

$$x\left(9-3x\right)=15-9x$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 9-3x.

$$9x-3x^{2}=15-9x$$

Me tāpiri te 9x ki ngā taha e rua.

$$9x-3x^{2}+9x=15$$

Pahekotia te 9x me 9x, ka 18x.

$$18x-3x^{2}=15$$

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.

$$-3x^{2}+18x=15$$

Whakawehea ngā taha e rua ki te -3.

$$\frac{-3x^{2}+18x}{-3}=\frac{15}{-3}$$

Mā te whakawehe ki te -3 ka wetekia te whakareanga ki te -3.

$$x^{2}+\frac{18}{-3}x=\frac{15}{-3}$$

Whakawehe 18 ki te -3.

$$x^{2}-6x=\frac{15}{-3}$$

Whakawehe 15 ki te -3.

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

Whakawehea te -6, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -3. Nā, tāpiria te pūrua o te -3 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-6x+\left(-3\right)^{2}=-5+\left(-3\right)^{2}$$

Pūrua -3.

$$x^{2}-6x+9=-5+9$$

Tāpiri -5 ki te 9.

$$x^{2}-6x+9=4$$

Tauwehea x^{2}-6x+9. 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}.

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

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

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

Whakarūnātia.

$$x-3=2 x-3=-2$$

Me tāpiri 3 ki ngā taha e rua o te whārite.

$$x=5 x=1$$