Whakaoti i te 6x^2+12x-11.34=0

$$6 { x }^{ 2 } +12x-11.34=0$$

Whakaoti mō x

$$x=0.7$$

$$x=-2.7$$

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.

$$6x^{2}+12x-11.34=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, 12 mō b, me -11.34 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-12±\sqrt{12^{2}-4\times 6\left(-11.34\right)}}{2\times 6}$$

Pūrua 12.

$$x=\frac{-12±\sqrt{144-4\times 6\left(-11.34\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{-12±\sqrt{144-24\left(-11.34\right)}}{2\times 6}$$

Whakareatia -24 ki te -11.34.

$$x=\frac{-12±\sqrt{144+272.16}}{2\times 6}$$

Tāpiri 144 ki te 272.16.

$$x=\frac{-12±\sqrt{416.16}}{2\times 6}$$

Tuhia te pūtakerua o te 416.16.

$$x=\frac{-12±\frac{102}{5}}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{-12±\frac{102}{5}}{12}$$

Nā, me whakaoti te whārite x=\frac{-12±\frac{102}{5}}{12} ina he tāpiri te ±. Tāpiri -12 ki te \frac{102}{5}.

$$x=\frac{\frac{42}{5}}{12}$$

Whakawehe \frac{42}{5} ki te 12.

$$x=\frac{7}{10}$$

Nā, me whakaoti te whārite x=\frac{-12±\frac{102}{5}}{12} ina he tango te ±. Tango \frac{102}{5} mai i -12.

$$x=-\frac{\frac{162}{5}}{12}$$

Whakawehe -\frac{162}{5} ki te 12.

$$x=-\frac{27}{10}$$

Kua oti te whārite te whakatau.

$$x=\frac{7}{10} x=-\frac{27}{10}$$

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.

$$6x^{2}+12x-11.34=0$$

Me tāpiri 11.34 ki ngā taha e rua o te whārite.

$$6x^{2}+12x-11.34-\left(-11.34\right)=-\left(-11.34\right)$$

Mā te tango i te -11.34 i a ia ake anō ka toe ko te 0.

$$6x^{2}+12x=-\left(-11.34\right)$$

Tango -11.34 mai i 0.

$$6x^{2}+12x=11.34$$

Whakawehea ngā taha e rua ki te 6.

$$\frac{6x^{2}+12x}{6}=\frac{11.34}{6}$$

Mā te whakawehe ki te 6 ka wetekia te whakareanga ki te 6.

$$x^{2}+\frac{12}{6}x=\frac{11.34}{6}$$

Whakawehe 12 ki te 6.

$$x^{2}+2x=\frac{11.34}{6}$$

Whakawehe 11.34 ki te 6.

$$x^{2}+2x=1.89$$

Whakawehea te 2, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 1. Nā, tāpiria te pūrua o te 1 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+2x+1^{2}=1.89+1^{2}$$

Pūrua 1.

$$x^{2}+2x+1=1.89+1$$

Tāpiri 1.89 ki te 1.

$$x^{2}+2x+1=2.89$$

Tauwehea x^{2}+2x+1. 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}.

$$\left(x+1\right)^{2}=2.89$$

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

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{2.89}$$

Whakarūnātia.

$$x+1=\frac{17}{10} x+1=-\frac{17}{10}$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$x=\frac{7}{10} x=-\frac{27}{10}$$