Whakaoti i te x^2-18x-18=-7

$$x ^ { 2 } - 18 x - 18 = - 7$$

Whakaoti mō x

$$x=2\sqrt{23}+9\approx 18.591663047$$

$$x=9-2\sqrt{23}\approx -0.591663047$$

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.

$$x^{2}-18x-18=-7$$

Me tāpiri 7 ki ngā taha e rua o te whārite.

$$x^{2}-18x-18-\left(-7\right)=-7-\left(-7\right)$$

Mā te tango i te -7 i a ia ake anō ka toe ko te 0.

$$x^{2}-18x-18-\left(-7\right)=0$$

Tango -7 mai i -18.

$$x^{2}-18x-11=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -18 mō b, me -11 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\left(-11\right)}}{2}$$

Pūrua -18.

$$x=\frac{-\left(-18\right)±\sqrt{324-4\left(-11\right)}}{2}$$

Whakareatia -4 ki te -11.

$$x=\frac{-\left(-18\right)±\sqrt{324+44}}{2}$$

Tāpiri 324 ki te 44.

$$x=\frac{-\left(-18\right)±\sqrt{368}}{2}$$

Tuhia te pūtakerua o te 368.

$$x=\frac{-\left(-18\right)±4\sqrt{23}}{2}$$

Ko te tauaro o -18 ko 18.

$$x=\frac{18±4\sqrt{23}}{2}$$

Nā, me whakaoti te whārite x=\frac{18±4\sqrt{23}}{2} ina he tāpiri te ±. Tāpiri 18 ki te 4\sqrt{23}.

$$x=\frac{4\sqrt{23}+18}{2}$$

Whakawehe 18+4\sqrt{23} ki te 2.

$$x=2\sqrt{23}+9$$

Nā, me whakaoti te whārite x=\frac{18±4\sqrt{23}}{2} ina he tango te ±. Tango 4\sqrt{23} mai i 18.

$$x=\frac{18-4\sqrt{23}}{2}$$

Whakawehe 18-4\sqrt{23} ki te 2.

$$x=9-2\sqrt{23}$$

Kua oti te whārite te whakatau.

$$x=2\sqrt{23}+9 x=9-2\sqrt{23}$$

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.

$$x^{2}-18x-18=-7$$

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

$$x^{2}-18x-18-\left(-18\right)=-7-\left(-18\right)$$

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

$$x^{2}-18x=-7-\left(-18\right)$$

Tango -18 mai i -7.

$$x^{2}-18x=11$$

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.

$$x^{2}-18x+\left(-9\right)^{2}=11+\left(-9\right)^{2}$$

Pūrua -9.

$$x^{2}-18x+81=11+81$$

Tāpiri 11 ki te 81.

$$x^{2}-18x+81=92$$

Tauwehea x^{2}-18x+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}.

$$\left(x-9\right)^{2}=92$$

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

$$\sqrt{\left(x-9\right)^{2}}=\sqrt{92}$$

Whakarūnātia.

$$x-9=2\sqrt{23} x-9=-2\sqrt{23}$$

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

$$x=2\sqrt{23}+9 x=9-2\sqrt{23}$$