Whakaoti i te q^2+6q-18=-5

$$q ^ { 2 } + 6 q - 18 = - 5$$

Whakaoti mō q (complex solution)

$$q=\sqrt{22}-3\approx 1.69041576$$

$$q=-\left(\sqrt{22}+3\right)\approx -7.69041576$$

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.

$$q^{2}+6q-18=-5$$

Me tāpiri 5 ki ngā taha e rua o te whārite.

$$q^{2}+6q-18-\left(-5\right)=-5-\left(-5\right)$$

Mā te tango i te -5 i a ia ake anō ka toe ko te 0.

$$q^{2}+6q-18-\left(-5\right)=0$$

Tango -5 mai i -18.

$$q^{2}+6q-13=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 6 mō b, me -13 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$q=\frac{-6±\sqrt{6^{2}-4\left(-13\right)}}{2}$$

Pūrua 6.

$$q=\frac{-6±\sqrt{36-4\left(-13\right)}}{2}$$

Whakareatia -4 ki te -13.

$$q=\frac{-6±\sqrt{36+52}}{2}$$

Tāpiri 36 ki te 52.

$$q=\frac{-6±\sqrt{88}}{2}$$

Tuhia te pūtakerua o te 88.

$$q=\frac{-6±2\sqrt{22}}{2}$$

Nā, me whakaoti te whārite q=\frac{-6±2\sqrt{22}}{2} ina he tāpiri te ±. Tāpiri -6 ki te 2\sqrt{22}.

$$q=\frac{2\sqrt{22}-6}{2}$$

Whakawehe -6+2\sqrt{22} ki te 2.

$$q=\sqrt{22}-3$$

Nā, me whakaoti te whārite q=\frac{-6±2\sqrt{22}}{2} ina he tango te ±. Tango 2\sqrt{22} mai i -6.

$$q=\frac{-2\sqrt{22}-6}{2}$$

Whakawehe -6-2\sqrt{22} ki te 2.

$$q=-\sqrt{22}-3$$

Kua oti te whārite te whakatau.

$$q=\sqrt{22}-3 q=-\sqrt{22}-3$$

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.

$$q^{2}+6q-18=-5$$

Me tāpiri 18 ki ngā taha e rua o te whārite.

$$q^{2}+6q-18-\left(-18\right)=-5-\left(-18\right)$$

Mā te tango i te -18 i a ia ake anō ka toe ko te 0.

$$q^{2}+6q=-5-\left(-18\right)$$

Tango -18 mai i -5.

$$q^{2}+6q=13$$

Whakawehea te 6, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 3. Nā, tāpiria te pūrua o te 3 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$q^{2}+6q+3^{2}=13+3^{2}$$

Pūrua 3.

$$q^{2}+6q+9=13+9$$

Tāpiri 13 ki te 9.

$$q^{2}+6q+9=22$$

Tauwehea q^{2}+6q+9. 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}.

$$\left(q+3\right)^{2}=22$$

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

$$\sqrt{\left(q+3\right)^{2}}=\sqrt{22}$$

Whakarūnātia.

$$q+3=\sqrt{22} q+3=-\sqrt{22}$$

Me tango 3 mai i ngā taha e rua o te whārite.

$$q=\sqrt{22}-3 q=-\sqrt{22}-3$$

Whakaoti mō q

$$q=\sqrt{22}-3\approx 1.69041576$$

$$q=-\sqrt{22}-3\approx -7.69041576$$

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.

$$q^{2}+6q-18=-5$$

Me tāpiri 5 ki ngā taha e rua o te whārite.

$$q^{2}+6q-18-\left(-5\right)=-5-\left(-5\right)$$

Mā te tango i te -5 i a ia ake anō ka toe ko te 0.

$$q^{2}+6q-18-\left(-5\right)=0$$

Tango -5 mai i -18.

$$q^{2}+6q-13=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 6 mō b, me -13 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$q=\frac{-6±\sqrt{6^{2}-4\left(-13\right)}}{2}$$

Pūrua 6.

$$q=\frac{-6±\sqrt{36-4\left(-13\right)}}{2}$$

Whakareatia -4 ki te -13.

$$q=\frac{-6±\sqrt{36+52}}{2}$$

Tāpiri 36 ki te 52.

$$q=\frac{-6±\sqrt{88}}{2}$$

Tuhia te pūtakerua o te 88.

$$q=\frac{-6±2\sqrt{22}}{2}$$

Nā, me whakaoti te whārite q=\frac{-6±2\sqrt{22}}{2} ina he tāpiri te ±. Tāpiri -6 ki te 2\sqrt{22}.

$$q=\frac{2\sqrt{22}-6}{2}$$

Whakawehe -6+2\sqrt{22} ki te 2.

$$q=\sqrt{22}-3$$

Nā, me whakaoti te whārite q=\frac{-6±2\sqrt{22}}{2} ina he tango te ±. Tango 2\sqrt{22} mai i -6.

$$q=\frac{-2\sqrt{22}-6}{2}$$

Whakawehe -6-2\sqrt{22} ki te 2.

$$q=-\sqrt{22}-3$$

Kua oti te whārite te whakatau.

$$q=\sqrt{22}-3 q=-\sqrt{22}-3$$

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.

$$q^{2}+6q-18=-5$$

Me tāpiri 18 ki ngā taha e rua o te whārite.

$$q^{2}+6q-18-\left(-18\right)=-5-\left(-18\right)$$

Mā te tango i te -18 i a ia ake anō ka toe ko te 0.

$$q^{2}+6q=-5-\left(-18\right)$$

Tango -18 mai i -5.

$$q^{2}+6q=13$$

Whakawehea te 6, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 3. Nā, tāpiria te pūrua o te 3 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$q^{2}+6q+3^{2}=13+3^{2}$$

Pūrua 3.

$$q^{2}+6q+9=13+9$$

Tāpiri 13 ki te 9.

$$q^{2}+6q+9=22$$

Tauwehea q^{2}+6q+9. 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}.

$$\left(q+3\right)^{2}=22$$

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

$$\sqrt{\left(q+3\right)^{2}}=\sqrt{22}$$

Whakarūnātia.

$$q+3=\sqrt{22} q+3=-\sqrt{22}$$

Me tango 3 mai i ngā taha e rua o te whārite.

$$q=\sqrt{22}-3 q=-\sqrt{22}-3$$