Whakaoti i te +(x)=x^2-36x

$$+ ( x ) = x ^ { 2 } - 36 x$$

Whakaoti mō x

$$x=37$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tangohia te x^{2} mai i ngā taha e rua.

$$x-x^{2}=-36x$$

Me tāpiri te 36x ki ngā taha e rua.

$$x-x^{2}+36x=0$$

Pahekotia te x me 36x, ka 37x.

$$37x-x^{2}=0$$

Tauwehea te x.

$$x\left(37-x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 37-x=0.

$$x=0 x=37$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te x^{2} mai i ngā taha e rua.

$$x-x^{2}=-36x$$

Me tāpiri te 36x ki ngā taha e rua.

$$x-x^{2}+36x=0$$

Pahekotia te x me 36x, ka 37x.

$$37x-x^{2}=0$$

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.

$$-x^{2}+37x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 37 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-37±\sqrt{37^{2}}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 37^{2}.

$$x=\frac{-37±37}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-37±37}{-2}$$

Nā, me whakaoti te whārite x=\frac{-37±37}{-2} ina he tāpiri te ±. Tāpiri -37 ki te 37.

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

Whakawehe 0 ki te -2.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-37±37}{-2} ina he tango te ±. Tango 37 mai i -37.

$$x=-\frac{74}{-2}$$

Whakawehe -74 ki te -2.

$$x=37$$

Kua oti te whārite te whakatau.

$$x=0 x=37$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te x^{2} mai i ngā taha e rua.

$$x-x^{2}=-36x$$

Me tāpiri te 36x ki ngā taha e rua.

$$x-x^{2}+36x=0$$

Pahekotia te x me 36x, ka 37x.

$$37x-x^{2}=0$$

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.

$$-x^{2}+37x=0$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}+37x}{-1}=\frac{0}{-1}$$

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

$$x^{2}+\frac{37}{-1}x=\frac{0}{-1}$$

Whakawehe 37 ki te -1.

$$x^{2}-37x=\frac{0}{-1}$$

Whakawehe 0 ki te -1.

$$x^{2}-37x=0$$

Whakawehea te -37, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{37}{2}. Nā, tāpiria te pūrua o te -\frac{37}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-37x+\left(-\frac{37}{2}\right)^{2}=\left(-\frac{37}{2}\right)^{2}$$

Pūruatia -\frac{37}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-37x+\frac{1369}{4}=\frac{1369}{4}$$

Tauwehea x^{2}-37x+\frac{1369}{4}. 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}.

$$\left(x-\frac{37}{2}\right)^{2}=\frac{1369}{4}$$

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

$$\sqrt{\left(x-\frac{37}{2}\right)^{2}}=\sqrt{\frac{1369}{4}}$$

Whakarūnātia.

$$x-\frac{37}{2}=\frac{37}{2} x-\frac{37}{2}=-\frac{37}{2}$$

Me tāpiri \frac{37}{2} ki ngā taha e rua o te whārite.

$$x=37 x=0$$