Whakaoti i te x^2+18x+81=-18+81

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

Whakaoti mō x

$$x=3\sqrt{7}-9\approx -1.062746067$$

$$x=-3\sqrt{7}-9\approx -16.937253933$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tāpirihia te -18 ki te 81, ka 63.

$$x^{2}+18x+81=63$$

Tangohia te 63 mai i ngā taha e rua.

$$x^{2}+18x+81-63=0$$

Tangohia te 63 i te 81, ka 18.

$$x^{2}+18x+18=0$$

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

$$x=\frac{-18±\sqrt{18^{2}-4\times 18}}{2}$$

Pūrua 18.

$$x=\frac{-18±\sqrt{324-4\times 18}}{2}$$

Whakareatia -4 ki te 18.

$$x=\frac{-18±\sqrt{324-72}}{2}$$

Tāpiri 324 ki te -72.

$$x=\frac{-18±\sqrt{252}}{2}$$

Tuhia te pūtakerua o te 252.

$$x=\frac{-18±6\sqrt{7}}{2}$$

Nā, me whakaoti te whārite x=\frac{-18±6\sqrt{7}}{2} ina he tāpiri te ±. Tāpiri -18 ki te 6\sqrt{7}.

$$x=\frac{6\sqrt{7}-18}{2}$$

Whakawehe -18+6\sqrt{7} ki te 2.

$$x=3\sqrt{7}-9$$

Nā, me whakaoti te whārite x=\frac{-18±6\sqrt{7}}{2} ina he tango te ±. Tango 6\sqrt{7} mai i -18.

$$x=\frac{-6\sqrt{7}-18}{2}$$

Whakawehe -18-6\sqrt{7} ki te 2.

$$x=-3\sqrt{7}-9$$

Kua oti te whārite te whakatau.

$$x=3\sqrt{7}-9 x=-3\sqrt{7}-9$$

Ngā Upane mō te Whakaoti i te Pūrua

Tāpiri -18 ki te 81.

$$x^{2}+18x+81=63$$

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}.

$$\left(x+9\right)^{2}=63$$

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

$$\sqrt{\left(x+9\right)^{2}}=\sqrt{63}$$

Whakarūnātia.

$$x+9=3\sqrt{7} x+9=-3\sqrt{7}$$

Me tango 9 mai i ngā taha e rua o te whārite.

$$x=3\sqrt{7}-9 x=-3\sqrt{7}-9$$