Whakaoti i te q^2-36q+540=3q^2-72q+540

$$q ^ { 2 } - 36 q + 540 = 3 q ^ { 2 } - 72 q + 540$$

Whakaoti mō q

$$q=18$$

$$q=0$$

Ngā Upane Whakamahi Tauwehe

Tangohia te 3q^{2} mai i ngā taha e rua.

$$q^{2}-36q+540-3q^{2}=-72q+540$$

Pahekotia te q^{2} me -3q^{2}, ka -2q^{2}.

$$-2q^{2}-36q+540=-72q+540$$

Me tāpiri te 72q ki ngā taha e rua.

$$-2q^{2}-36q+540+72q=540$$

Pahekotia te -36q me 72q, ka 36q.

$$-2q^{2}+36q+540=540$$

Tangohia te 540 mai i ngā taha e rua.

$$-2q^{2}+36q+540-540=0$$

Tangohia te 540 i te 540, ka 0.

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

Tauwehea te q.

$$q\left(-2q+36\right)=0$$

Hei kimi otinga whārite, me whakaoti te q=0 me te -2q+36=0.

$$q=0 q=18$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 3q^{2} mai i ngā taha e rua.

$$q^{2}-36q+540-3q^{2}=-72q+540$$

Pahekotia te q^{2} me -3q^{2}, ka -2q^{2}.

$$-2q^{2}-36q+540=-72q+540$$

Me tāpiri te 72q ki ngā taha e rua.

$$-2q^{2}-36q+540+72q=540$$

Pahekotia te -36q me 72q, ka 36q.

$$-2q^{2}+36q+540=540$$

Tangohia te 540 mai i ngā taha e rua.

$$-2q^{2}+36q+540-540=0$$

Tangohia te 540 i te 540, ka 0.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -2 mō a, 36 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$q=\frac{-36±\sqrt{36^{2}}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te 36^{2}.

$$q=\frac{-36±36}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$q=\frac{-36±36}{-4}$$

Nā, me whakaoti te whārite q=\frac{-36±36}{-4} ina he tāpiri te ±. Tāpiri -36 ki te 36.

$$q=\frac{0}{-4}$$

Whakawehe 0 ki te -4.

$$q=0$$

Nā, me whakaoti te whārite q=\frac{-36±36}{-4} ina he tango te ±. Tango 36 mai i -36.

$$q=-\frac{72}{-4}$$

Whakawehe -72 ki te -4.

$$q=18$$

Kua oti te whārite te whakatau.

$$q=0 q=18$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 3q^{2} mai i ngā taha e rua.

$$q^{2}-36q+540-3q^{2}=-72q+540$$

Pahekotia te q^{2} me -3q^{2}, ka -2q^{2}.

$$-2q^{2}-36q+540=-72q+540$$

Me tāpiri te 72q ki ngā taha e rua.

$$-2q^{2}-36q+540+72q=540$$

Pahekotia te -36q me 72q, ka 36q.

$$-2q^{2}+36q+540=540$$

Tangohia te 540 mai i ngā taha e rua.

$$-2q^{2}+36q=540-540$$

Tangohia te 540 i te 540, ka 0.

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

Whakawehea ngā taha e rua ki te -2.

$$\frac{-2q^{2}+36q}{-2}=\frac{0}{-2}$$

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

$$q^{2}+\frac{36}{-2}q=\frac{0}{-2}$$

Whakawehe 36 ki te -2.

$$q^{2}-18q=\frac{0}{-2}$$

Whakawehe 0 ki te -2.

$$q^{2}-18q=0$$

Whakawehea te -18, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -9. Nā, tāpiria te pūrua o te -9 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$q^{2}-18q+\left(-9\right)^{2}=\left(-9\right)^{2}$$

Pūrua -9.

$$q^{2}-18q+81=81$$

Tauwehea q^{2}-18q+81. 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}.

$$\left(q-9\right)^{2}=81$$

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

$$\sqrt{\left(q-9\right)^{2}}=\sqrt{81}$$

Whakarūnātia.

$$q-9=9 q-9=-9$$

Me tāpiri 9 ki ngā taha e rua o te whārite.

$$q=18 q=0$$