Whakaoti i te 11=x^2-3x-4

$$11 = x ^ { 2 } - 3 x - 4$$

Whakaoti mō x

$$x = \frac{\sqrt{69} + 3}{2} \approx 5.653311931$$

$$x=\frac{3-\sqrt{69}}{2}\approx -2.653311931$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{2}-3x-4=11$$

Tangohia te 11 mai i ngā taha e rua.

$$x^{2}-3x-4-11=0$$

Tangohia te 11 i te -4, ka -15.

$$x^{2}-3x-15=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -3 mō b, me -15 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\left(-15\right)}}{2}$$

Pūrua -3.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\left(-15\right)}}{2}$$

Whakareatia -4 ki te -15.

$$x=\frac{-\left(-3\right)±\sqrt{9+60}}{2}$$

Tāpiri 9 ki te 60.

$$x=\frac{-\left(-3\right)±\sqrt{69}}{2}$$

Ko te tauaro o -3 ko 3.

$$x=\frac{3±\sqrt{69}}{2}$$

Nā, me whakaoti te whārite x=\frac{3±\sqrt{69}}{2} ina he tāpiri te ±. Tāpiri 3 ki te \sqrt{69}.

$$x=\frac{\sqrt{69}+3}{2}$$

Nā, me whakaoti te whārite x=\frac{3±\sqrt{69}}{2} ina he tango te ±. Tango \sqrt{69} mai i 3.

$$x=\frac{3-\sqrt{69}}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{69}+3}{2} x=\frac{3-\sqrt{69}}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{2}-3x-4=11$$

Me tāpiri te 4 ki ngā taha e rua.

$$x^{2}-3x=11+4$$

Tāpirihia te 11 ki te 4, ka 15.

$$x^{2}-3x=15$$

Whakawehea te -3, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{3}{2}. Nā, tāpiria te pūrua o te -\frac{3}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-3x+\left(-\frac{3}{2}\right)^{2}=15+\left(-\frac{3}{2}\right)^{2}$$

Pūruatia -\frac{3}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-3x+\frac{9}{4}=15+\frac{9}{4}$$

Tāpiri 15 ki te \frac{9}{4}.

$$x^{2}-3x+\frac{9}{4}=\frac{69}{4}$$

Tauwehea x^{2}-3x+\frac{9}{4}. 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}.

$$\left(x-\frac{3}{2}\right)^{2}=\frac{69}{4}$$

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

$$\sqrt{\left(x-\frac{3}{2}\right)^{2}}=\sqrt{\frac{69}{4}}$$

Whakarūnātia.

$$x-\frac{3}{2}=\frac{\sqrt{69}}{2} x-\frac{3}{2}=-\frac{\sqrt{69}}{2}$$

Me tāpiri \frac{3}{2} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{69}+3}{2} x=\frac{3-\sqrt{69}}{2}$$