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

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

Whakaoti mō x

$$x = \frac{\sqrt{157} - 5}{6} \approx 1.254994014$$

$$x=\frac{-\sqrt{157}-5}{6}\approx -2.921660681$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 2x mai i ngā taha e rua.

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

Pahekotia te -3x me -2x, ka -5x.

$$-3x^{2}-5x+11=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -3 mō a, -5 mō b, me 11 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\left(-3\right)\times 11}}{2\left(-3\right)}$$

Pūrua -5.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\left(-3\right)\times 11}}{2\left(-3\right)}$$

Whakareatia -4 ki te -3.

$$x=\frac{-\left(-5\right)±\sqrt{25+12\times 11}}{2\left(-3\right)}$$

Whakareatia 12 ki te 11.

$$x=\frac{-\left(-5\right)±\sqrt{25+132}}{2\left(-3\right)}$$

Tāpiri 25 ki te 132.

$$x=\frac{-\left(-5\right)±\sqrt{157}}{2\left(-3\right)}$$

Ko te tauaro o -5 ko 5.

$$x=\frac{5±\sqrt{157}}{2\left(-3\right)}$$

Whakareatia 2 ki te -3.

$$x=\frac{5±\sqrt{157}}{-6}$$

Nā, me whakaoti te whārite x=\frac{5±\sqrt{157}}{-6} ina he tāpiri te ±. Tāpiri 5 ki te \sqrt{157}.

$$x=\frac{\sqrt{157}+5}{-6}$$

Whakawehe 5+\sqrt{157} ki te -6.

$$x=\frac{-\sqrt{157}-5}{6}$$

Nā, me whakaoti te whārite x=\frac{5±\sqrt{157}}{-6} ina he tango te ±. Tango \sqrt{157} mai i 5.

$$x=\frac{5-\sqrt{157}}{-6}$$

Whakawehe 5-\sqrt{157} ki te -6.

$$x=\frac{\sqrt{157}-5}{6}$$

Kua oti te whārite te whakatau.

$$x=\frac{-\sqrt{157}-5}{6} x=\frac{\sqrt{157}-5}{6}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 2x mai i ngā taha e rua.

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

Pahekotia te -3x me -2x, ka -5x.

$$-3x^{2}-5x+11=0$$

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

$$-3x^{2}-5x=-11$$

Whakawehea ngā taha e rua ki te -3.

$$\frac{-3x^{2}-5x}{-3}=-\frac{11}{-3}$$

Mā te whakawehe ki te -3 ka wetekia te whakareanga ki te -3.

$$x^{2}+\left(-\frac{5}{-3}\right)x=-\frac{11}{-3}$$

Whakawehe -5 ki te -3.

$$x^{2}+\frac{5}{3}x=-\frac{11}{-3}$$

Whakawehe -11 ki te -3.

$$x^{2}+\frac{5}{3}x=\frac{11}{3}$$

Whakawehea te \frac{5}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{5}{6}. Nā, tāpiria te pūrua o te \frac{5}{6} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{5}{3}x+\left(\frac{5}{6}\right)^{2}=\frac{11}{3}+\left(\frac{5}{6}\right)^{2}$$

Pūruatia \frac{5}{6} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{5}{3}x+\frac{25}{36}=\frac{11}{3}+\frac{25}{36}$$

Tāpiri \frac{11}{3} ki te \frac{25}{36} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}+\frac{5}{3}x+\frac{25}{36}=\frac{157}{36}$$

Tauwehea x^{2}+\frac{5}{3}x+\frac{25}{36}. 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}.

$$\left(x+\frac{5}{6}\right)^{2}=\frac{157}{36}$$

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

$$\sqrt{\left(x+\frac{5}{6}\right)^{2}}=\sqrt{\frac{157}{36}}$$

Whakarūnātia.

$$x+\frac{5}{6}=\frac{\sqrt{157}}{6} x+\frac{5}{6}=-\frac{\sqrt{157}}{6}$$

Me tango \frac{5}{6} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{157}-5}{6} x=\frac{-\sqrt{157}-5}{6}$$