Whakaoti i te x^2+67=18x

$$x ^ { 2 } + 67 = 18 x$$

Whakaoti mō x

$$x=\sqrt{14}+9\approx 12.741657387$$

$$x=9-\sqrt{14}\approx 5.258342613$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 18x mai i ngā taha e rua.

$$x^{2}+67-18x=0$$

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.

$$x^{2}-18x+67=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -18 mō b, me 67 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\times 67}}{2}$$

Pūrua -18.

$$x=\frac{-\left(-18\right)±\sqrt{324-4\times 67}}{2}$$

Whakareatia -4 ki te 67.

$$x=\frac{-\left(-18\right)±\sqrt{324-268}}{2}$$

Tāpiri 324 ki te -268.

$$x=\frac{-\left(-18\right)±\sqrt{56}}{2}$$

Tuhia te pūtakerua o te 56.

$$x=\frac{-\left(-18\right)±2\sqrt{14}}{2}$$

Ko te tauaro o -18 ko 18.

$$x=\frac{18±2\sqrt{14}}{2}$$

Nā, me whakaoti te whārite x=\frac{18±2\sqrt{14}}{2} ina he tāpiri te ±. Tāpiri 18 ki te 2\sqrt{14}.

$$x=\frac{2\sqrt{14}+18}{2}$$

Whakawehe 18+2\sqrt{14} ki te 2.

$$x=\sqrt{14}+9$$

Nā, me whakaoti te whārite x=\frac{18±2\sqrt{14}}{2} ina he tango te ±. Tango 2\sqrt{14} mai i 18.

$$x=\frac{18-2\sqrt{14}}{2}$$

Whakawehe 18-2\sqrt{14} ki te 2.

$$x=9-\sqrt{14}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{14}+9 x=9-\sqrt{14}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 18x mai i ngā taha e rua.

$$x^{2}+67-18x=0$$

Tangohia te 67 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x^{2}-18x=-67$$

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.

$$x^{2}-18x+\left(-9\right)^{2}=-67+\left(-9\right)^{2}$$

Pūrua -9.

$$x^{2}-18x+81=-67+81$$

Tāpiri -67 ki te 81.

$$x^{2}-18x+81=14$$

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}.

$$\left(x-9\right)^{2}=14$$

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

$$\sqrt{\left(x-9\right)^{2}}=\sqrt{14}$$

Whakarūnātia.

$$x-9=\sqrt{14} x-9=-\sqrt{14}$$

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

$$x=\sqrt{14}+9 x=9-\sqrt{14}$$