Whakaoti i te x^2+x^2-11x-60=08

$$x ^ { 2 } + x ^ { 2 } - 11 x - 60 = 08$$

Whakaoti mō x

$$x = \frac{\sqrt{601} + 11}{4} \approx 8.878825336$$

$$x=\frac{11-\sqrt{601}}{4}\approx -3.378825336$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te x^{2} me x^{2}, ka 2x^{2}.

$$2x^{2}-11x-60=0\times 8$$

Whakareatia te 0 ki te 8, ka 0.

$$2x^{2}-11x-60=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, -11 mō b, me -60 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-11\right)±\sqrt{\left(-11\right)^{2}-4\times 2\left(-60\right)}}{2\times 2}$$

Pūrua -11.

$$x=\frac{-\left(-11\right)±\sqrt{121-4\times 2\left(-60\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-\left(-11\right)±\sqrt{121-8\left(-60\right)}}{2\times 2}$$

Whakareatia -8 ki te -60.

$$x=\frac{-\left(-11\right)±\sqrt{121+480}}{2\times 2}$$

Tāpiri 121 ki te 480.

$$x=\frac{-\left(-11\right)±\sqrt{601}}{2\times 2}$$

Ko te tauaro o -11 ko 11.

$$x=\frac{11±\sqrt{601}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{11±\sqrt{601}}{4}$$

Nā, me whakaoti te whārite x=\frac{11±\sqrt{601}}{4} ina he tāpiri te ±. Tāpiri 11 ki te \sqrt{601}.

$$x=\frac{\sqrt{601}+11}{4}$$

Nā, me whakaoti te whārite x=\frac{11±\sqrt{601}}{4} ina he tango te ±. Tango \sqrt{601} mai i 11.

$$x=\frac{11-\sqrt{601}}{4}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{601}+11}{4} x=\frac{11-\sqrt{601}}{4}$$

Ngā Upane mō te Whakaoti i te Pūrua

Pahekotia te x^{2} me x^{2}, ka 2x^{2}.

$$2x^{2}-11x-60=0\times 8$$

Whakareatia te 0 ki te 8, ka 0.

$$2x^{2}-11x-60=0$$

Me tāpiri te 60 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$2x^{2}-11x=60$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}-11x}{2}=\frac{60}{2}$$

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

$$x^{2}-\frac{11}{2}x=\frac{60}{2}$$

Whakawehe 60 ki te 2.

$$x^{2}-\frac{11}{2}x=30$$

Whakawehea te -\frac{11}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{11}{4}. Nā, tāpiria te pūrua o te -\frac{11}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{11}{2}x+\left(-\frac{11}{4}\right)^{2}=30+\left(-\frac{11}{4}\right)^{2}$$

Pūruatia -\frac{11}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{11}{2}x+\frac{121}{16}=30+\frac{121}{16}$$

Tāpiri 30 ki te \frac{121}{16}.

$$x^{2}-\frac{11}{2}x+\frac{121}{16}=\frac{601}{16}$$

Tauwehea x^{2}-\frac{11}{2}x+\frac{121}{16}. 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}.

$$\left(x-\frac{11}{4}\right)^{2}=\frac{601}{16}$$

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

$$\sqrt{\left(x-\frac{11}{4}\right)^{2}}=\sqrt{\frac{601}{16}}$$

Whakarūnātia.

$$x-\frac{11}{4}=\frac{\sqrt{601}}{4} x-\frac{11}{4}=-\frac{\sqrt{601}}{4}$$

Me tāpiri \frac{11}{4} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{601}+11}{4} x=\frac{11-\sqrt{601}}{4}$$