Whakaoti i te 36=left(2x+12right)left(x+1right)

$$36 = \left( 2x+12 \right) \left( x+1 \right)$$

Whakaoti mō x

$$x = \frac{\sqrt{97} - 7}{2} \approx 1.424428901$$

$$x=\frac{-\sqrt{97}-7}{2}\approx -8.424428901$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 2x+12 ki te x+1 ka whakakotahi i ngā kupu rite.

$$36=2x^{2}+14x+12$$

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

$$2x^{2}+14x+12=36$$

Tangohia te 36 mai i ngā taha e rua.

$$2x^{2}+14x+12-36=0$$

Tangohia te 36 i te 12, ka -24.

$$2x^{2}+14x-24=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 14 mō b, me -24 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-14±\sqrt{14^{2}-4\times 2\left(-24\right)}}{2\times 2}$$

Pūrua 14.

$$x=\frac{-14±\sqrt{196-4\times 2\left(-24\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-14±\sqrt{196-8\left(-24\right)}}{2\times 2}$$

Whakareatia -8 ki te -24.

$$x=\frac{-14±\sqrt{196+192}}{2\times 2}$$

Tāpiri 196 ki te 192.

$$x=\frac{-14±\sqrt{388}}{2\times 2}$$

Tuhia te pūtakerua o te 388.

$$x=\frac{-14±2\sqrt{97}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-14±2\sqrt{97}}{4}$$

Nā, me whakaoti te whārite x=\frac{-14±2\sqrt{97}}{4} ina he tāpiri te ±. Tāpiri -14 ki te 2\sqrt{97}.

$$x=\frac{2\sqrt{97}-14}{4}$$

Whakawehe -14+2\sqrt{97} ki te 4.

$$x=\frac{\sqrt{97}-7}{2}$$

Nā, me whakaoti te whārite x=\frac{-14±2\sqrt{97}}{4} ina he tango te ±. Tango 2\sqrt{97} mai i -14.

$$x=\frac{-2\sqrt{97}-14}{4}$$

Whakawehe -14-2\sqrt{97} ki te 4.

$$x=\frac{-\sqrt{97}-7}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{97}-7}{2} x=\frac{-\sqrt{97}-7}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 2x+12 ki te x+1 ka whakakotahi i ngā kupu rite.

$$36=2x^{2}+14x+12$$

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

$$2x^{2}+14x+12=36$$

Tangohia te 12 mai i ngā taha e rua.

$$2x^{2}+14x=36-12$$

Tangohia te 12 i te 36, ka 24.

$$2x^{2}+14x=24$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}+14x}{2}=\frac{24}{2}$$

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

$$x^{2}+\frac{14}{2}x=\frac{24}{2}$$

Whakawehe 14 ki te 2.

$$x^{2}+7x=\frac{24}{2}$$

Whakawehe 24 ki te 2.

$$x^{2}+7x=12$$

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

$$x^{2}+7x+\left(\frac{7}{2}\right)^{2}=12+\left(\frac{7}{2}\right)^{2}$$

Pūruatia \frac{7}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+7x+\frac{49}{4}=12+\frac{49}{4}$$

Tāpiri 12 ki te \frac{49}{4}.

$$x^{2}+7x+\frac{49}{4}=\frac{97}{4}$$

Tauwehea x^{2}+7x+\frac{49}{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}.

$$\left(x+\frac{7}{2}\right)^{2}=\frac{97}{4}$$

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

$$\sqrt{\left(x+\frac{7}{2}\right)^{2}}=\sqrt{\frac{97}{4}}$$

Whakarūnātia.

$$x+\frac{7}{2}=\frac{\sqrt{97}}{2} x+\frac{7}{2}=-\frac{\sqrt{97}}{2}$$

Me tango \frac{7}{2} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{97}-7}{2} x=\frac{-\sqrt{97}-7}{2}$$