Whakaoti i te x^2+18x-95=0

$${ x }^{ 2 } +18x-95=0$$

Whakaoti mō x

$$x=4\sqrt{11}-9\approx 4.266499161$$

$$x=-4\sqrt{11}-9\approx -22.266499161$$

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.

$$x^{2}+18x-95=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 18 mō b, me -95 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-18±\sqrt{18^{2}-4\left(-95\right)}}{2}$$

Pūrua 18.

$$x=\frac{-18±\sqrt{324-4\left(-95\right)}}{2}$$

Whakareatia -4 ki te -95.

$$x=\frac{-18±\sqrt{324+380}}{2}$$

Tāpiri 324 ki te 380.

$$x=\frac{-18±\sqrt{704}}{2}$$

Tuhia te pūtakerua o te 704.

$$x=\frac{-18±8\sqrt{11}}{2}$$

Nā, me whakaoti te whārite x=\frac{-18±8\sqrt{11}}{2} ina he tāpiri te ±. Tāpiri -18 ki te 8\sqrt{11}.

$$x=\frac{8\sqrt{11}-18}{2}$$

Whakawehe -18+8\sqrt{11} ki te 2.

$$x=4\sqrt{11}-9$$

Nā, me whakaoti te whārite x=\frac{-18±8\sqrt{11}}{2} ina he tango te ±. Tango 8\sqrt{11} mai i -18.

$$x=\frac{-8\sqrt{11}-18}{2}$$

Whakawehe -18-8\sqrt{11} ki te 2.

$$x=-4\sqrt{11}-9$$

Kua oti te whārite te whakatau.

$$x=4\sqrt{11}-9 x=-4\sqrt{11}-9$$

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.

$$x^{2}+18x-95=0$$

Me tāpiri 95 ki ngā taha e rua o te whārite.

$$x^{2}+18x-95-\left(-95\right)=-\left(-95\right)$$

Mā te tango i te -95 i a ia ake anō ka toe ko te 0.

$$x^{2}+18x=-\left(-95\right)$$

Tango -95 mai i 0.

$$x^{2}+18x=95$$

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.

$$x^{2}+18x+9^{2}=95+9^{2}$$

Pūrua 9.

$$x^{2}+18x+81=95+81$$

Tāpiri 95 ki te 81.

$$x^{2}+18x+81=176$$

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}.

$$\left(x+9\right)^{2}=176$$

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

$$\sqrt{\left(x+9\right)^{2}}=\sqrt{176}$$

Whakarūnātia.

$$x+9=4\sqrt{11} x+9=-4\sqrt{11}$$

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

$$x=4\sqrt{11}-9 x=-4\sqrt{11}-9$$