Whakaoti i te q^2+22q-25=0

$$q ^ { 2 } + 22 q - 25 = 0$$

Whakaoti mō q

$$q=\sqrt{146}-11\approx 1.083045974$$

$$q=-\sqrt{146}-11\approx -23.083045974$$

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.

$$q^{2}+22q-25=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 22 mō b, me -25 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$q=\frac{-22±\sqrt{22^{2}-4\left(-25\right)}}{2}$$

Pūrua 22.

$$q=\frac{-22±\sqrt{484-4\left(-25\right)}}{2}$$

Whakareatia -4 ki te -25.

$$q=\frac{-22±\sqrt{484+100}}{2}$$

Tāpiri 484 ki te 100.

$$q=\frac{-22±\sqrt{584}}{2}$$

Tuhia te pūtakerua o te 584.

$$q=\frac{-22±2\sqrt{146}}{2}$$

Nā, me whakaoti te whārite q=\frac{-22±2\sqrt{146}}{2} ina he tāpiri te ±. Tāpiri -22 ki te 2\sqrt{146}.

$$q=\frac{2\sqrt{146}-22}{2}$$

Whakawehe -22+2\sqrt{146} ki te 2.

$$q=\sqrt{146}-11$$

Nā, me whakaoti te whārite q=\frac{-22±2\sqrt{146}}{2} ina he tango te ±. Tango 2\sqrt{146} mai i -22.

$$q=\frac{-2\sqrt{146}-22}{2}$$

Whakawehe -22-2\sqrt{146} ki te 2.

$$q=-\sqrt{146}-11$$

Kua oti te whārite te whakatau.

$$q=\sqrt{146}-11 q=-\sqrt{146}-11$$

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.

$$q^{2}+22q-25=0$$

Me tāpiri 25 ki ngā taha e rua o te whārite.

$$q^{2}+22q-25-\left(-25\right)=-\left(-25\right)$$

Mā te tango i te -25 i a ia ake anō ka toe ko te 0.

$$q^{2}+22q=-\left(-25\right)$$

Tango -25 mai i 0.

$$q^{2}+22q=25$$

Whakawehea te 22, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 11. Nā, tāpiria te pūrua o te 11 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$q^{2}+22q+11^{2}=25+11^{2}$$

Pūrua 11.

$$q^{2}+22q+121=25+121$$

Tāpiri 25 ki te 121.

$$q^{2}+22q+121=146$$

Tauwehea q^{2}+22q+121. 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}.

$$\left(q+11\right)^{2}=146$$

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

$$\sqrt{\left(q+11\right)^{2}}=\sqrt{146}$$

Whakarūnātia.

$$q+11=\sqrt{146} q+11=-\sqrt{146}$$

Me tango 11 mai i ngā taha e rua o te whārite.

$$q=\sqrt{146}-11 q=-\sqrt{146}-11$$