Whakaoti i te 6^2=x(x-3)

$${ 6 }^{ 2 } =x(x-3)$$

Whakaoti mō x

$$x = \frac{3 \sqrt{17} + 3}{2} \approx 7.684658438$$

$$x=\frac{3-3\sqrt{17}}{2}\approx -4.684658438$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 6 mā te pū o 2, kia riro ko 36.

$$36=x\left(x-3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x-3.

$$36=x^{2}-3x$$

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

$$x^{2}-3x=36$$

Tangohia te 36 mai i ngā taha e rua.

$$x^{2}-3x-36=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -3 mō b, me -36 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\left(-36\right)}}{2}$$

Pūrua -3.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\left(-36\right)}}{2}$$

Whakareatia -4 ki te -36.

$$x=\frac{-\left(-3\right)±\sqrt{9+144}}{2}$$

Tāpiri 9 ki te 144.

$$x=\frac{-\left(-3\right)±\sqrt{153}}{2}$$

Tuhia te pūtakerua o te 153.

$$x=\frac{-\left(-3\right)±3\sqrt{17}}{2}$$

Ko te tauaro o -3 ko 3.

$$x=\frac{3±3\sqrt{17}}{2}$$

Nā, me whakaoti te whārite x=\frac{3±3\sqrt{17}}{2} ina he tāpiri te ±. Tāpiri 3 ki te 3\sqrt{17}.

$$x=\frac{3\sqrt{17}+3}{2}$$

Nā, me whakaoti te whārite x=\frac{3±3\sqrt{17}}{2} ina he tango te ±. Tango 3\sqrt{17} mai i 3.

$$x=\frac{3-3\sqrt{17}}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{3\sqrt{17}+3}{2} x=\frac{3-3\sqrt{17}}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tātaihia te 6 mā te pū o 2, kia riro ko 36.

$$36=x\left(x-3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x-3.

$$36=x^{2}-3x$$

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

$$x^{2}-3x=36$$

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

$$x^{2}-3x+\left(-\frac{3}{2}\right)^{2}=36+\left(-\frac{3}{2}\right)^{2}$$

Pūruatia -\frac{3}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-3x+\frac{9}{4}=36+\frac{9}{4}$$

Tāpiri 36 ki te \frac{9}{4}.

$$x^{2}-3x+\frac{9}{4}=\frac{153}{4}$$

Tauwehea x^{2}-3x+\frac{9}{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}.

$$\left(x-\frac{3}{2}\right)^{2}=\frac{153}{4}$$

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

$$\sqrt{\left(x-\frac{3}{2}\right)^{2}}=\sqrt{\frac{153}{4}}$$

Whakarūnātia.

$$x-\frac{3}{2}=\frac{3\sqrt{17}}{2} x-\frac{3}{2}=-\frac{3\sqrt{17}}{2}$$

Me tāpiri \frac{3}{2} ki ngā taha e rua o te whārite.

$$x=\frac{3\sqrt{17}+3}{2} x=\frac{3-3\sqrt{17}}{2}$$