Whakaoti i te x^2+4/57(x/2)div11=3

$$x ^ { 2 } + \frac { 4 } { 5 } 7 ( \frac { x } { 2 } ) \div 11 = 3$$

Whakaoti mō x

$$x = \frac{2 \sqrt{2281} - 7}{55} \approx 1.609447845$$

$$x=\frac{-2\sqrt{2281}-7}{55}\approx -1.8639933$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te 11.

$$11x^{2}+\frac{4}{5}\times 7\times \frac{x}{2}=33$$

Whakareatia te \frac{4}{5} ki te 7, ka \frac{28}{5}.

$$11x^{2}+\frac{28}{5}\times \frac{x}{2}=33$$

Me whakarea te \frac{28}{5} ki te \frac{x}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$11x^{2}+\frac{28x}{5\times 2}=33$$

Me whakakore tahi te 2 i te taurunga me te tauraro.

$$11x^{2}+\frac{14x}{5}=33$$

Tangohia te 33 mai i ngā taha e rua.

$$11x^{2}+\frac{14x}{5}-33=0$$

Whakareatia ngā taha e rua o te whārite ki te 5.

$$55x^{2}+14x-165=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 55 mō a, 14 mō b, me -165 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-14±\sqrt{14^{2}-4\times 55\left(-165\right)}}{2\times 55}$$

Pūrua 14.

$$x=\frac{-14±\sqrt{196-4\times 55\left(-165\right)}}{2\times 55}$$

Whakareatia -4 ki te 55.

$$x=\frac{-14±\sqrt{196-220\left(-165\right)}}{2\times 55}$$

Whakareatia -220 ki te -165.

$$x=\frac{-14±\sqrt{196+36300}}{2\times 55}$$

Tāpiri 196 ki te 36300.

$$x=\frac{-14±\sqrt{36496}}{2\times 55}$$

Tuhia te pūtakerua o te 36496.

$$x=\frac{-14±4\sqrt{2281}}{2\times 55}$$

Whakareatia 2 ki te 55.

$$x=\frac{-14±4\sqrt{2281}}{110}$$

Nā, me whakaoti te whārite x=\frac{-14±4\sqrt{2281}}{110} ina he tāpiri te ±. Tāpiri -14 ki te 4\sqrt{2281}.

$$x=\frac{4\sqrt{2281}-14}{110}$$

Whakawehe -14+4\sqrt{2281} ki te 110.

$$x=\frac{2\sqrt{2281}-7}{55}$$

Nā, me whakaoti te whārite x=\frac{-14±4\sqrt{2281}}{110} ina he tango te ±. Tango 4\sqrt{2281} mai i -14.

$$x=\frac{-4\sqrt{2281}-14}{110}$$

Whakawehe -14-4\sqrt{2281} ki te 110.

$$x=\frac{-2\sqrt{2281}-7}{55}$$

Kua oti te whārite te whakatau.

$$x=\frac{2\sqrt{2281}-7}{55} x=\frac{-2\sqrt{2281}-7}{55}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia ngā taha e rua o te whārite ki te 11.

$$11x^{2}+\frac{4}{5}\times 7\times \frac{x}{2}=33$$

Whakareatia te \frac{4}{5} ki te 7, ka \frac{28}{5}.

$$11x^{2}+\frac{28}{5}\times \frac{x}{2}=33$$

Me whakarea te \frac{28}{5} ki te \frac{x}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$11x^{2}+\frac{28x}{5\times 2}=33$$

Me whakakore tahi te 2 i te taurunga me te tauraro.

$$11x^{2}+\frac{14x}{5}=33$$

Whakareatia ngā taha e rua o te whārite ki te 5.

$$55x^{2}+14x=165$$

Whakawehea ngā taha e rua ki te 55.

$$\frac{55x^{2}+14x}{55}=\frac{165}{55}$$

Mā te whakawehe ki te 55 ka wetekia te whakareanga ki te 55.

$$x^{2}+\frac{14}{55}x=\frac{165}{55}$$

Whakawehe 165 ki te 55.

$$x^{2}+\frac{14}{55}x=3$$

Whakawehea te \frac{14}{55}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{7}{55}. Nā, tāpiria te pūrua o te \frac{7}{55} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{14}{55}x+\left(\frac{7}{55}\right)^{2}=3+\left(\frac{7}{55}\right)^{2}$$

Pūruatia \frac{7}{55} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{14}{55}x+\frac{49}{3025}=3+\frac{49}{3025}$$

Tāpiri 3 ki te \frac{49}{3025}.

$$x^{2}+\frac{14}{55}x+\frac{49}{3025}=\frac{9124}{3025}$$

Tauwehea x^{2}+\frac{14}{55}x+\frac{49}{3025}. 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}.

$$\left(x+\frac{7}{55}\right)^{2}=\frac{9124}{3025}$$

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

$$\sqrt{\left(x+\frac{7}{55}\right)^{2}}=\sqrt{\frac{9124}{3025}}$$

Whakarūnātia.

$$x+\frac{7}{55}=\frac{2\sqrt{2281}}{55} x+\frac{7}{55}=-\frac{2\sqrt{2281}}{55}$$

Me tango \frac{7}{55} mai i ngā taha e rua o te whārite.

$$x=\frac{2\sqrt{2281}-7}{55} x=\frac{-2\sqrt{2281}-7}{55}$$