Whakaoti i te x^2+140x=261

$$x ^ { 2 } + 140 x = 261$$

Whakaoti mō x (complex solution)

$$x=\sqrt{5161}-70\approx 1.840100223$$

$$x=-\left(\sqrt{5161}+70\right)\approx -141.840100223$$

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.

$$x^{2}+140x=261$$

Me tango 261 mai i ngā taha e rua o te whārite.

$$x^{2}+140x-261=261-261$$

Mā te tango i te 261 i a ia ake anō ka toe ko te 0.

$$x^{2}+140x-261=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 140 mō b, me -261 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-140±\sqrt{140^{2}-4\left(-261\right)}}{2}$$

Pūrua 140.

$$x=\frac{-140±\sqrt{19600-4\left(-261\right)}}{2}$$

Whakareatia -4 ki te -261.

$$x=\frac{-140±\sqrt{19600+1044}}{2}$$

Tāpiri 19600 ki te 1044.

$$x=\frac{-140±\sqrt{20644}}{2}$$

Tuhia te pūtakerua o te 20644.

$$x=\frac{-140±2\sqrt{5161}}{2}$$

Nā, me whakaoti te whārite x=\frac{-140±2\sqrt{5161}}{2} ina he tāpiri te ±. Tāpiri -140 ki te 2\sqrt{5161}.

$$x=\frac{2\sqrt{5161}-140}{2}$$

Whakawehe -140+2\sqrt{5161} ki te 2.

$$x=\sqrt{5161}-70$$

Nā, me whakaoti te whārite x=\frac{-140±2\sqrt{5161}}{2} ina he tango te ±. Tango 2\sqrt{5161} mai i -140.

$$x=\frac{-2\sqrt{5161}-140}{2}$$

Whakawehe -140-2\sqrt{5161} ki te 2.

$$x=-\sqrt{5161}-70$$

Kua oti te whārite te whakatau.

$$x=\sqrt{5161}-70 x=-\sqrt{5161}-70$$

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.

$$x^{2}+140x=261$$

Whakawehea te 140, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 70. Nā, tāpiria te pūrua o te 70 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+140x+70^{2}=261+70^{2}$$

Pūrua 70.

$$x^{2}+140x+4900=261+4900$$

Tāpiri 261 ki te 4900.

$$x^{2}+140x+4900=5161$$

Tauwehea x^{2}+140x+4900. 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}.

$$\left(x+70\right)^{2}=5161$$

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

$$\sqrt{\left(x+70\right)^{2}}=\sqrt{5161}$$

Whakarūnātia.

$$x+70=\sqrt{5161} x+70=-\sqrt{5161}$$

Me tango 70 mai i ngā taha e rua o te whārite.

$$x=\sqrt{5161}-70 x=-\sqrt{5161}-70$$

Whakaoti mō x

$$x=\sqrt{5161}-70\approx 1.840100223$$

$$x=-\sqrt{5161}-70\approx -141.840100223$$

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.

$$x^{2}+140x=261$$

Me tango 261 mai i ngā taha e rua o te whārite.

$$x^{2}+140x-261=261-261$$

Mā te tango i te 261 i a ia ake anō ka toe ko te 0.

$$x^{2}+140x-261=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 140 mō b, me -261 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-140±\sqrt{140^{2}-4\left(-261\right)}}{2}$$

Pūrua 140.

$$x=\frac{-140±\sqrt{19600-4\left(-261\right)}}{2}$$

Whakareatia -4 ki te -261.

$$x=\frac{-140±\sqrt{19600+1044}}{2}$$

Tāpiri 19600 ki te 1044.

$$x=\frac{-140±\sqrt{20644}}{2}$$

Tuhia te pūtakerua o te 20644.

$$x=\frac{-140±2\sqrt{5161}}{2}$$

Nā, me whakaoti te whārite x=\frac{-140±2\sqrt{5161}}{2} ina he tāpiri te ±. Tāpiri -140 ki te 2\sqrt{5161}.

$$x=\frac{2\sqrt{5161}-140}{2}$$

Whakawehe -140+2\sqrt{5161} ki te 2.

$$x=\sqrt{5161}-70$$

Nā, me whakaoti te whārite x=\frac{-140±2\sqrt{5161}}{2} ina he tango te ±. Tango 2\sqrt{5161} mai i -140.

$$x=\frac{-2\sqrt{5161}-140}{2}$$

Whakawehe -140-2\sqrt{5161} ki te 2.

$$x=-\sqrt{5161}-70$$

Kua oti te whārite te whakatau.

$$x=\sqrt{5161}-70 x=-\sqrt{5161}-70$$

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.

$$x^{2}+140x=261$$

Whakawehea te 140, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 70. Nā, tāpiria te pūrua o te 70 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+140x+70^{2}=261+70^{2}$$

Pūrua 70.

$$x^{2}+140x+4900=261+4900$$

Tāpiri 261 ki te 4900.

$$x^{2}+140x+4900=5161$$

Tauwehea x^{2}+140x+4900. 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}.

$$\left(x+70\right)^{2}=5161$$

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

$$\sqrt{\left(x+70\right)^{2}}=\sqrt{5161}$$

Whakarūnātia.

$$x+70=\sqrt{5161} x+70=-\sqrt{5161}$$

Me tango 70 mai i ngā taha e rua o te whārite.

$$x=\sqrt{5161}-70 x=-\sqrt{5161}-70$$