Whakaoti i te (x+7)x=13*2

$$( x + 7 ) x = 13 \cdot 2$$

Whakaoti mō x

$$x = \frac{3 \sqrt{17} - 7}{2} \approx 2.684658438$$

$$x=\frac{-3\sqrt{17}-7}{2}\approx -9.684658438$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x+7 ki te x.

$$x^{2}+7x=13\times 2$$

Whakareatia te 13 ki te 2, ka 26.

$$x^{2}+7x=26$$

Tangohia te 26 mai i ngā taha e rua.

$$x^{2}+7x-26=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 7 mō b, me -26 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-7±\sqrt{7^{2}-4\left(-26\right)}}{2}$$

Pūrua 7.

$$x=\frac{-7±\sqrt{49-4\left(-26\right)}}{2}$$

Whakareatia -4 ki te -26.

$$x=\frac{-7±\sqrt{49+104}}{2}$$

Tāpiri 49 ki te 104.

$$x=\frac{-7±\sqrt{153}}{2}$$

Tuhia te pūtakerua o te 153.

$$x=\frac{-7±3\sqrt{17}}{2}$$

Nā, me whakaoti te whārite x=\frac{-7±3\sqrt{17}}{2} ina he tāpiri te ±. Tāpiri -7 ki te 3\sqrt{17}.

$$x=\frac{3\sqrt{17}-7}{2}$$

Nā, me whakaoti te whārite x=\frac{-7±3\sqrt{17}}{2} ina he tango te ±. Tango 3\sqrt{17} mai i -7.

$$x=\frac{-3\sqrt{17}-7}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{3\sqrt{17}-7}{2} x=\frac{-3\sqrt{17}-7}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x+7 ki te x.

$$x^{2}+7x=13\times 2$$

Whakareatia te 13 ki te 2, ka 26.

$$x^{2}+7x=26$$

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.

$$x^{2}+7x+\left(\frac{7}{2}\right)^{2}=26+\left(\frac{7}{2}\right)^{2}$$

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

$$x^{2}+7x+\frac{49}{4}=26+\frac{49}{4}$$

Tāpiri 26 ki te \frac{49}{4}.

$$x^{2}+7x+\frac{49}{4}=\frac{153}{4}$$

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}.

$$\left(x+\frac{7}{2}\right)^{2}=\frac{153}{4}$$

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

$$\sqrt{\left(x+\frac{7}{2}\right)^{2}}=\sqrt{\frac{153}{4}}$$

Whakarūnātia.

$$x+\frac{7}{2}=\frac{3\sqrt{17}}{2} x+\frac{7}{2}=-\frac{3\sqrt{17}}{2}$$

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

$$x=\frac{3\sqrt{17}-7}{2} x=\frac{-3\sqrt{17}-7}{2}$$