Whakaoti i te 0.5x^2+8x-12=0

$$0.5 { x }^{ 2 } +8x-12 = 0$$

Whakaoti mō x

$$x=2\sqrt{22}-8\approx 1.38083152$$

$$x=-2\sqrt{22}-8\approx -17.38083152$$

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.

$$\frac{1}{2}x^{2}+8x-12=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi \frac{1}{2} mō a, 8 mō b, me -12 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\times \frac{1}{2}\left(-12\right)}}{2\times \frac{1}{2}}$$

Pūrua 8.

$$x=\frac{-8±\sqrt{64-4\times \frac{1}{2}\left(-12\right)}}{2\times \frac{1}{2}}$$

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

$$x=\frac{-8±\sqrt{64-2\left(-12\right)}}{2\times \frac{1}{2}}$$

Whakareatia -2 ki te -12.

$$x=\frac{-8±\sqrt{64+24}}{2\times \frac{1}{2}}$$

Tāpiri 64 ki te 24.

$$x=\frac{-8±\sqrt{88}}{2\times \frac{1}{2}}$$

Tuhia te pūtakerua o te 88.

$$x=\frac{-8±2\sqrt{22}}{2\times \frac{1}{2}}$$

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

$$x=\frac{-8±2\sqrt{22}}{1}$$

Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{22}}{1} ina he tāpiri te ±. Tāpiri -8 ki te 2\sqrt{22}.

$$x=\frac{2\sqrt{22}-8}{1}$$

Whakawehe -8+2\sqrt{22} ki te 1.

$$x=2\sqrt{22}-8$$

Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{22}}{1} ina he tango te ±. Tango 2\sqrt{22} mai i -8.

$$x=\frac{-2\sqrt{22}-8}{1}$$

Whakawehe -8-2\sqrt{22} ki te 1.

$$x=-2\sqrt{22}-8$$

Kua oti te whārite te whakatau.

$$x=2\sqrt{22}-8 x=-2\sqrt{22}-8$$

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.

$$\frac{1}{2}x^{2}+8x-12=0$$

Me tāpiri 12 ki ngā taha e rua o te whārite.

$$\frac{1}{2}x^{2}+8x-12-\left(-12\right)=-\left(-12\right)$$

Mā te tango i te -12 i a ia ake anō ka toe ko te 0.

$$\frac{1}{2}x^{2}+8x=-\left(-12\right)$$

Tango -12 mai i 0.

$$\frac{1}{2}x^{2}+8x=12$$

Me whakarea ngā taha e rua ki te 2.

$$\frac{\frac{1}{2}x^{2}+8x}{\frac{1}{2}}=\frac{12}{\frac{1}{2}}$$

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

$$x^{2}+\frac{8}{\frac{1}{2}}x=\frac{12}{\frac{1}{2}}$$

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

$$x^{2}+16x=\frac{12}{\frac{1}{2}}$$

Whakawehe 12 ki te \frac{1}{2} mā te whakarea 12 ki te tau huripoki o \frac{1}{2}.

$$x^{2}+16x=24$$

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.

$$x^{2}+16x+8^{2}=24+8^{2}$$

Pūrua 8.

$$x^{2}+16x+64=24+64$$

Tāpiri 24 ki te 64.

$$x^{2}+16x+64=88$$

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}.

$$\left(x+8\right)^{2}=88$$

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

$$\sqrt{\left(x+8\right)^{2}}=\sqrt{88}$$

Whakarūnātia.

$$x+8=2\sqrt{22} x+8=-2\sqrt{22}$$

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

$$x=2\sqrt{22}-8 x=-2\sqrt{22}-8$$