Whakaoti i te 0.5x^2+8x-2=0

$$0.5 { x }^{ 2 } +8x-2 = 0$$

Whakaoti mō x

$$x=2\sqrt{17}-8\approx 0.246211251$$

$$x=-2\sqrt{17}-8\approx -16.246211251$$

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.

$$\frac{1}{2}x^{2}+8x-2=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi \frac{1}{2} mō a, 8 mō b, me -2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\times \frac{1}{2}\left(-2\right)}}{2\times \frac{1}{2}}$$

Pūrua 8.

$$x=\frac{-8±\sqrt{64-4\times \frac{1}{2}\left(-2\right)}}{2\times \frac{1}{2}}$$

Whakareatia -4 ki te \frac{1}{2}.

$$x=\frac{-8±\sqrt{64-2\left(-2\right)}}{2\times \frac{1}{2}}$$

Whakareatia -2 ki te -2.

$$x=\frac{-8±\sqrt{64+4}}{2\times \frac{1}{2}}$$

Tāpiri 64 ki te 4.

$$x=\frac{-8±\sqrt{68}}{2\times \frac{1}{2}}$$

Tuhia te pūtakerua o te 68.

$$x=\frac{-8±2\sqrt{17}}{2\times \frac{1}{2}}$$

Whakareatia 2 ki te \frac{1}{2}.

$$x=\frac{-8±2\sqrt{17}}{1}$$

Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{17}}{1} ina he tāpiri te ±. Tāpiri -8 ki te 2\sqrt{17}.

$$x=\frac{2\sqrt{17}-8}{1}$$

Whakawehe -8+2\sqrt{17} ki te 1.

$$x=2\sqrt{17}-8$$

Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{17}}{1} ina he tango te ±. Tango 2\sqrt{17} mai i -8.

$$x=\frac{-2\sqrt{17}-8}{1}$$

Whakawehe -8-2\sqrt{17} ki te 1.

$$x=-2\sqrt{17}-8$$

Kua oti te whārite te whakatau.

$$x=2\sqrt{17}-8 x=-2\sqrt{17}-8$$

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.

$$\frac{1}{2}x^{2}+8x-2=0$$

Me tāpiri 2 ki ngā taha e rua o te whārite.

$$\frac{1}{2}x^{2}+8x-2-\left(-2\right)=-\left(-2\right)$$

Mā te tango i te -2 i a ia ake anō ka toe ko te 0.

$$\frac{1}{2}x^{2}+8x=-\left(-2\right)$$

Tango -2 mai i 0.

$$\frac{1}{2}x^{2}+8x=2$$

Me whakarea ngā taha e rua ki te 2.

$$\frac{\frac{1}{2}x^{2}+8x}{\frac{1}{2}}=\frac{2}{\frac{1}{2}}$$

Mā te whakawehe ki te \frac{1}{2} ka wetekia te whakareanga ki te \frac{1}{2}.

$$x^{2}+\frac{8}{\frac{1}{2}}x=\frac{2}{\frac{1}{2}}$$

Whakawehe 8 ki te \frac{1}{2} mā te whakarea 8 ki te tau huripoki o \frac{1}{2}.

$$x^{2}+16x=\frac{2}{\frac{1}{2}}$$

Whakawehe 2 ki te \frac{1}{2} mā te whakarea 2 ki te tau huripoki o \frac{1}{2}.

$$x^{2}+16x=4$$

Whakawehea te 16, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 8. Nā, tāpiria te pūrua o te 8 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+16x+8^{2}=4+8^{2}$$

Pūrua 8.

$$x^{2}+16x+64=4+64$$

Tāpiri 4 ki te 64.

$$x^{2}+16x+64=68$$

Tauwehea x^{2}+16x+64. 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}.

$$\left(x+8\right)^{2}=68$$

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

$$\sqrt{\left(x+8\right)^{2}}=\sqrt{68}$$

Whakarūnātia.

$$x+8=2\sqrt{17} x+8=-2\sqrt{17}$$

Me tango 8 mai i ngā taha e rua o te whārite.

$$x=2\sqrt{17}-8 x=-2\sqrt{17}-8$$