Whakaoti i te -x^2+28x=0

$$- { x }^{ 2 } +28x = 0$$

Whakaoti mō x

$$x=28$$

$$x=0$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$-x^{2}+28x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 28 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-28±\sqrt{28^{2}}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 28^{2}.

$$x=\frac{-28±28}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-28±28}{-2}$$

Nā, me whakaoti te whārite x=\frac{-28±28}{-2} ina he tāpiri te ±. Tāpiri -28 ki te 28.

$$x=\frac{0}{-2}$$

Whakawehe 0 ki te -2.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-28±28}{-2} ina he tango te ±. Tango 28 mai i -28.

$$x=-\frac{56}{-2}$$

Whakawehe -56 ki te -2.

$$x=28$$

Kua oti te whārite te whakatau.

$$x=0 x=28$$

Ngā Upane mō te Whakaoti i te Pūrua

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.

$$-x^{2}+28x=0$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}+28x}{-1}=\frac{0}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$x^{2}+\frac{28}{-1}x=\frac{0}{-1}$$

Whakawehe 28 ki te -1.

$$x^{2}-28x=\frac{0}{-1}$$

Whakawehe 0 ki te -1.

$$x^{2}-28x=0$$

Whakawehea te -28, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -14. Nā, tāpiria te pūrua o te -14 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-28x+\left(-14\right)^{2}=\left(-14\right)^{2}$$

Pūrua -14.

$$x^{2}-28x+196=196$$

Tauwehea x^{2}-28x+196. 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}.

$$\left(x-14\right)^{2}=196$$

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

$$\sqrt{\left(x-14\right)^{2}}=\sqrt{196}$$

Whakarūnātia.

$$x-14=14 x-14=-14$$

Me tāpiri 14 ki ngā taha e rua o te whārite.

$$x=28 x=0$$