Whakaoti i te 913=81+x^2-8x

$$913 = 81 + x ^ { 2 } - 8 x$$

Whakaoti mō x

$$x=4\sqrt{53}+4\approx 33.120439557$$

$$x=4-4\sqrt{53}\approx -25.120439557$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$81+x^{2}-8x=913$$

Tangohia te 913 mai i ngā taha e rua.

$$81+x^{2}-8x-913=0$$

Tangohia te 913 i te 81, ka -832.

$$-832+x^{2}-8x=0$$

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.

$$x^{2}-8x-832=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -8 mō b, me -832 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\left(-832\right)}}{2}$$

Pūrua -8.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\left(-832\right)}}{2}$$

Whakareatia -4 ki te -832.

$$x=\frac{-\left(-8\right)±\sqrt{64+3328}}{2}$$

Tāpiri 64 ki te 3328.

$$x=\frac{-\left(-8\right)±\sqrt{3392}}{2}$$

Tuhia te pūtakerua o te 3392.

$$x=\frac{-\left(-8\right)±8\sqrt{53}}{2}$$

Ko te tauaro o -8 ko 8.

$$x=\frac{8±8\sqrt{53}}{2}$$

Nā, me whakaoti te whārite x=\frac{8±8\sqrt{53}}{2} ina he tāpiri te ±. Tāpiri 8 ki te 8\sqrt{53}.

$$x=\frac{8\sqrt{53}+8}{2}$$

Whakawehe 8+8\sqrt{53} ki te 2.

$$x=4\sqrt{53}+4$$

Nā, me whakaoti te whārite x=\frac{8±8\sqrt{53}}{2} ina he tango te ±. Tango 8\sqrt{53} mai i 8.

$$x=\frac{8-8\sqrt{53}}{2}$$

Whakawehe 8-8\sqrt{53} ki te 2.

$$x=4-4\sqrt{53}$$

Kua oti te whārite te whakatau.

$$x=4\sqrt{53}+4 x=4-4\sqrt{53}$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$81+x^{2}-8x=913$$

Tangohia te 81 mai i ngā taha e rua.

$$x^{2}-8x=913-81$$

Tangohia te 81 i te 913, ka 832.

$$x^{2}-8x=832$$

Whakawehea te -8, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -4. Nā, tāpiria te pūrua o te -4 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-8x+\left(-4\right)^{2}=832+\left(-4\right)^{2}$$

Pūrua -4.

$$x^{2}-8x+16=832+16$$

Tāpiri 832 ki te 16.

$$x^{2}-8x+16=848$$

Tauwehea x^{2}-8x+16. 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}.

$$\left(x-4\right)^{2}=848$$

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

$$\sqrt{\left(x-4\right)^{2}}=\sqrt{848}$$

Whakarūnātia.

$$x-4=4\sqrt{53} x-4=-4\sqrt{53}$$

Me tāpiri 4 ki ngā taha e rua o te whārite.

$$x=4\sqrt{53}+4 x=4-4\sqrt{53}$$