Whakaoti i te x(x+7)/2=34

$$\frac { x ( x + 7 ) } { 2 } = 34$$

Whakaoti mō x

$$x = \frac{\sqrt{321} - 7}{2} \approx 5.458236434$$

$$x=\frac{-\sqrt{321}-7}{2}\approx -12.458236434$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me whakarea ngā taha e rua ki te 2.

$$x\left(x+7\right)=34\times 2$$

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

$$x^{2}+7x=34\times 2$$

Whakareatia te 34 ki te 2, ka 68.

$$x^{2}+7x=68$$

Tangohia te 68 mai i ngā taha e rua.

$$x^{2}+7x-68=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 7 mō b, me -68 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-7±\sqrt{7^{2}-4\left(-68\right)}}{2}$$

Pūrua 7.

$$x=\frac{-7±\sqrt{49-4\left(-68\right)}}{2}$$

Whakareatia -4 ki te -68.

$$x=\frac{-7±\sqrt{49+272}}{2}$$

Tāpiri 49 ki te 272.

$$x=\frac{-7±\sqrt{321}}{2}$$

Nā, me whakaoti te whārite x=\frac{-7±\sqrt{321}}{2} ina he tāpiri te ±. Tāpiri -7 ki te \sqrt{321}.

$$x=\frac{\sqrt{321}-7}{2}$$

Nā, me whakaoti te whārite x=\frac{-7±\sqrt{321}}{2} ina he tango te ±. Tango \sqrt{321} mai i -7.

$$x=\frac{-\sqrt{321}-7}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{321}-7}{2} x=\frac{-\sqrt{321}-7}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Me whakarea ngā taha e rua ki te 2.

$$x\left(x+7\right)=34\times 2$$

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

$$x^{2}+7x=34\times 2$$

Whakareatia te 34 ki te 2, ka 68.

$$x^{2}+7x=68$$

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.

$$x^{2}+7x+\left(\frac{7}{2}\right)^{2}=68+\left(\frac{7}{2}\right)^{2}$$

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

$$x^{2}+7x+\frac{49}{4}=68+\frac{49}{4}$$

Tāpiri 68 ki te \frac{49}{4}.

$$x^{2}+7x+\frac{49}{4}=\frac{321}{4}$$

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}.

$$\left(x+\frac{7}{2}\right)^{2}=\frac{321}{4}$$

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

$$\sqrt{\left(x+\frac{7}{2}\right)^{2}}=\sqrt{\frac{321}{4}}$$

Whakarūnātia.

$$x+\frac{7}{2}=\frac{\sqrt{321}}{2} x+\frac{7}{2}=-\frac{\sqrt{321}}{2}$$

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

$$x=\frac{\sqrt{321}-7}{2} x=\frac{-\sqrt{321}-7}{2}$$