Whakaoti i te 4x+11=2x^2

$$4 x + 11 = 2 x ^ { 2 }$$

Whakaoti mō x

$$x=\frac{\sqrt{26}}{2}+1\approx 3.549509757$$

$$x=-\frac{\sqrt{26}}{2}+1\approx -1.549509757$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 2x^{2} mai i ngā taha e rua.

$$4x+11-2x^{2}=0$$

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.

$$-2x^{2}+4x+11=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -2 mō a, 4 mō b, me 11 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-4±\sqrt{4^{2}-4\left(-2\right)\times 11}}{2\left(-2\right)}$$

Pūrua 4.

$$x=\frac{-4±\sqrt{16-4\left(-2\right)\times 11}}{2\left(-2\right)}$$

Whakareatia -4 ki te -2.

$$x=\frac{-4±\sqrt{16+8\times 11}}{2\left(-2\right)}$$

Whakareatia 8 ki te 11.

$$x=\frac{-4±\sqrt{16+88}}{2\left(-2\right)}$$

Tāpiri 16 ki te 88.

$$x=\frac{-4±\sqrt{104}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te 104.

$$x=\frac{-4±2\sqrt{26}}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=\frac{-4±2\sqrt{26}}{-4}$$

Nā, me whakaoti te whārite x=\frac{-4±2\sqrt{26}}{-4} ina he tāpiri te ±. Tāpiri -4 ki te 2\sqrt{26}.

$$x=\frac{2\sqrt{26}-4}{-4}$$

Whakawehe -4+2\sqrt{26} ki te -4.

$$x=-\frac{\sqrt{26}}{2}+1$$

Nā, me whakaoti te whārite x=\frac{-4±2\sqrt{26}}{-4} ina he tango te ±. Tango 2\sqrt{26} mai i -4.

$$x=\frac{-2\sqrt{26}-4}{-4}$$

Whakawehe -4-2\sqrt{26} ki te -4.

$$x=\frac{\sqrt{26}}{2}+1$$

Kua oti te whārite te whakatau.

$$x=-\frac{\sqrt{26}}{2}+1 x=\frac{\sqrt{26}}{2}+1$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 2x^{2} mai i ngā taha e rua.

$$4x+11-2x^{2}=0$$

Tangohia te 11 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$4x-2x^{2}=-11$$

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.

$$-2x^{2}+4x=-11$$

Whakawehea ngā taha e rua ki te -2.

$$\frac{-2x^{2}+4x}{-2}=-\frac{11}{-2}$$

Mā te whakawehe ki te -2 ka wetekia te whakareanga ki te -2.

$$x^{2}+\frac{4}{-2}x=-\frac{11}{-2}$$

Whakawehe 4 ki te -2.

$$x^{2}-2x=-\frac{11}{-2}$$

Whakawehe -11 ki te -2.

$$x^{2}-2x=\frac{11}{2}$$

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.

$$x^{2}-2x+1=\frac{11}{2}+1$$

Tāpiri \frac{11}{2} ki te 1.

$$x^{2}-2x+1=\frac{13}{2}$$

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}.

$$\left(x-1\right)^{2}=\frac{13}{2}$$

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

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{\frac{13}{2}}$$

Whakarūnātia.

$$x-1=\frac{\sqrt{26}}{2} x-1=-\frac{\sqrt{26}}{2}$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{26}}{2}+1 x=-\frac{\sqrt{26}}{2}+1$$