Whakaoti i te x(16-0.5x)-120=0

$$x(16-0.5x)-120=0$$

Whakaoti mō x

$$x=12$$

$$x=20$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 16-0.5x.

$$16x-0.5x^{2}-120=0$$

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.

$$-0.5x^{2}+16x-120=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -0.5 mō a, 16 mō b, me -120 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-16±\sqrt{16^{2}-4\left(-0.5\right)\left(-120\right)}}{2\left(-0.5\right)}$$

Pūrua 16.

$$x=\frac{-16±\sqrt{256-4\left(-0.5\right)\left(-120\right)}}{2\left(-0.5\right)}$$

Whakareatia -4 ki te -0.5.

$$x=\frac{-16±\sqrt{256+2\left(-120\right)}}{2\left(-0.5\right)}$$

Whakareatia 2 ki te -120.

$$x=\frac{-16±\sqrt{256-240}}{2\left(-0.5\right)}$$

Tāpiri 256 ki te -240.

$$x=\frac{-16±\sqrt{16}}{2\left(-0.5\right)}$$

Tuhia te pūtakerua o te 16.

$$x=\frac{-16±4}{2\left(-0.5\right)}$$

Whakareatia 2 ki te -0.5.

$$x=\frac{-16±4}{-1}$$

Nā, me whakaoti te whārite x=\frac{-16±4}{-1} ina he tāpiri te ±. Tāpiri -16 ki te 4.

$$x=-\frac{12}{-1}$$

Whakawehe -12 ki te -1.

$$x=12$$

Nā, me whakaoti te whārite x=\frac{-16±4}{-1} ina he tango te ±. Tango 4 mai i -16.

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

Whakawehe -20 ki te -1.

$$x=20$$

Kua oti te whārite te whakatau.

$$x=12 x=20$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 16-0.5x.

$$16x-0.5x^{2}-120=0$$

Me tāpiri te 120 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$16x-0.5x^{2}=120$$

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.

$$-0.5x^{2}+16x=120$$

Me whakarea ngā taha e rua ki te -2.

$$\frac{-0.5x^{2}+16x}{-0.5}=\frac{120}{-0.5}$$

Mā te whakawehe ki te -0.5 ka wetekia te whakareanga ki te -0.5.

$$x^{2}+\frac{16}{-0.5}x=\frac{120}{-0.5}$$

Whakawehe 16 ki te -0.5 mā te whakarea 16 ki te tau huripoki o -0.5.

$$x^{2}-32x=\frac{120}{-0.5}$$

Whakawehe 120 ki te -0.5 mā te whakarea 120 ki te tau huripoki o -0.5.

$$x^{2}-32x=-240$$

Whakawehea te -32, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -16. Nā, tāpiria te pūrua o te -16 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-32x+\left(-16\right)^{2}=-240+\left(-16\right)^{2}$$

Pūrua -16.

$$x^{2}-32x+256=-240+256$$

Tāpiri -240 ki te 256.

$$x^{2}-32x+256=16$$

Tauwehea x^{2}-32x+256. 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}.

$$\left(x-16\right)^{2}=16$$

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

$$\sqrt{\left(x-16\right)^{2}}=\sqrt{16}$$

Whakarūnātia.

$$x-16=4 x-16=-4$$

Me tāpiri 16 ki ngā taha e rua o te whārite.

$$x=20 x=12$$