Whakaoti i te 14x+4.8+2.4x=x^2+2x

$$14 x + 4.8 + 2.4 x = x ^ { 2 } + 2 x$$

Whakaoti mō x

$$x = \frac{2 \sqrt{354} + 36}{5} \approx 14.725955089$$

$$x=\frac{36-2\sqrt{354}}{5}\approx -0.325955089$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te 14x me 2.4x, ka 16.4x.

$$16.4x+4.8=x^{2}+2x$$

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

$$16.4x+4.8-x^{2}=2x$$

Tangohia te 2x mai i ngā taha e rua.

$$16.4x+4.8-x^{2}-2x=0$$

Pahekotia te 16.4x me -2x, ka 14.4x.

$$14.4x+4.8-x^{2}=0$$

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.

$$-x^{2}+14.4x+4.8=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 14.4 mō b, me 4.8 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-14.4±\sqrt{14.4^{2}-4\left(-1\right)\times 4.8}}{2\left(-1\right)}$$

Pūruatia 14.4 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-14.4±\sqrt{207.36-4\left(-1\right)\times 4.8}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-14.4±\sqrt{207.36+4\times 4.8}}{2\left(-1\right)}$$

Whakareatia 4 ki te 4.8.

$$x=\frac{-14.4±\sqrt{207.36+19.2}}{2\left(-1\right)}$$

Tāpiri 207.36 ki te 19.2 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.

$$x=\frac{-14.4±\sqrt{226.56}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 226.56.

$$x=\frac{-14.4±\frac{4\sqrt{354}}{5}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-14.4±\frac{4\sqrt{354}}{5}}{-2}$$

Nā, me whakaoti te whārite x=\frac{-14.4±\frac{4\sqrt{354}}{5}}{-2} ina he tāpiri te ±. Tāpiri -14.4 ki te \frac{4\sqrt{354}}{5}.

$$x=\frac{4\sqrt{354}-72}{-2\times 5}$$

Whakawehe \frac{-72+4\sqrt{354}}{5} ki te -2.

$$x=\frac{36-2\sqrt{354}}{5}$$

Nā, me whakaoti te whārite x=\frac{-14.4±\frac{4\sqrt{354}}{5}}{-2} ina he tango te ±. Tango \frac{4\sqrt{354}}{5} mai i -14.4.

$$x=\frac{-4\sqrt{354}-72}{-2\times 5}$$

Whakawehe \frac{-72-4\sqrt{354}}{5} ki te -2.

$$x=\frac{2\sqrt{354}+36}{5}$$

Kua oti te whārite te whakatau.

$$x=\frac{36-2\sqrt{354}}{5} x=\frac{2\sqrt{354}+36}{5}$$

Ngā Upane mō te Whakaoti i te Pūrua

Pahekotia te 14x me 2.4x, ka 16.4x.

$$16.4x+4.8=x^{2}+2x$$

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

$$16.4x+4.8-x^{2}=2x$$

Tangohia te 2x mai i ngā taha e rua.

$$16.4x+4.8-x^{2}-2x=0$$

Pahekotia te 16.4x me -2x, ka 14.4x.

$$14.4x+4.8-x^{2}=0$$

Tangohia te 4.8 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$14.4x-x^{2}=-4.8$$

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.

$$-x^{2}+14.4x=-4.8$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}+14.4x}{-1}=-\frac{4.8}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$x^{2}+\frac{14.4}{-1}x=-\frac{4.8}{-1}$$

Whakawehe 14.4 ki te -1.

$$x^{2}-14.4x=-\frac{4.8}{-1}$$

Whakawehe -4.8 ki te -1.

$$x^{2}-14.4x=4.8$$

Whakawehea te -14.4, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -7.2. Nā, tāpiria te pūrua o te -7.2 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-14.4x+\left(-7.2\right)^{2}=4.8+\left(-7.2\right)^{2}$$

Pūruatia -7.2 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-14.4x+51.84=4.8+51.84$$

Tāpiri 4.8 ki te 51.84 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.

$$x^{2}-14.4x+51.84=56.64$$

Tauwehea x^{2}-14.4x+51.84. 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}.

$$\left(x-7.2\right)^{2}=56.64$$

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

$$\sqrt{\left(x-7.2\right)^{2}}=\sqrt{56.64}$$

Whakarūnātia.

$$x-7.2=\frac{2\sqrt{354}}{5} x-7.2=-\frac{2\sqrt{354}}{5}$$

Me tāpiri 7.2 ki ngā taha e rua o te whārite.

$$x=\frac{2\sqrt{354}+36}{5} x=\frac{36-2\sqrt{354}}{5}$$