Whakaoti i te x^2=3x*7(14x+32)*954

$${ x }^{ 2 } =3x \times 7(14x+32) \times 954$$

Whakaoti mō x

$$x = -\frac{641088}{280475} = -2\frac{80138}{280475} \approx -2.285722435$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Whakareatia te 3 ki te 7, ka 21.

$$x^{2}=21x\left(14x+32\right)\times 954$$

Whakareatia te 21 ki te 954, ka 20034.

$$x^{2}=20034x\left(14x+32\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 20034x ki te 14x+32.

$$x^{2}=280476x^{2}+641088x$$

Tangohia te 280476x^{2} mai i ngā taha e rua.

$$x^{2}-280476x^{2}=641088x$$

Pahekotia te x^{2} me -280476x^{2}, ka -280475x^{2}.

$$-280475x^{2}=641088x$$

Tangohia te 641088x mai i ngā taha e rua.

$$-280475x^{2}-641088x=0$$

Tauwehea te x.

$$x\left(-280475x-641088\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te -280475x-641088=0.

$$x=0 x=-\frac{641088}{280475}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 3 ki te 7, ka 21.

$$x^{2}=21x\left(14x+32\right)\times 954$$

Whakareatia te 21 ki te 954, ka 20034.

$$x^{2}=20034x\left(14x+32\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 20034x ki te 14x+32.

$$x^{2}=280476x^{2}+641088x$$

Tangohia te 280476x^{2} mai i ngā taha e rua.

$$x^{2}-280476x^{2}=641088x$$

Pahekotia te x^{2} me -280476x^{2}, ka -280475x^{2}.

$$-280475x^{2}=641088x$$

Tangohia te 641088x mai i ngā taha e rua.

$$-280475x^{2}-641088x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -280475 mō a, -641088 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-641088\right)±\sqrt{\left(-641088\right)^{2}}}{2\left(-280475\right)}$$

Tuhia te pūtakerua o te \left(-641088\right)^{2}.

$$x=\frac{-\left(-641088\right)±641088}{2\left(-280475\right)}$$

Ko te tauaro o -641088 ko 641088.

$$x=\frac{641088±641088}{2\left(-280475\right)}$$

Whakareatia 2 ki te -280475.

$$x=\frac{641088±641088}{-560950}$$

Nā, me whakaoti te whārite x=\frac{641088±641088}{-560950} ina he tāpiri te ±. Tāpiri 641088 ki te 641088.

$$x=\frac{1282176}{-560950}$$

Whakahekea te hautanga \frac{1282176}{-560950} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=-\frac{641088}{280475}$$

Nā, me whakaoti te whārite x=\frac{641088±641088}{-560950} ina he tango te ±. Tango 641088 mai i 641088.

$$x=\frac{0}{-560950}$$

Whakawehe 0 ki te -560950.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=-\frac{641088}{280475} x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te 3 ki te 7, ka 21.

$$x^{2}=21x\left(14x+32\right)\times 954$$

Whakareatia te 21 ki te 954, ka 20034.

$$x^{2}=20034x\left(14x+32\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 20034x ki te 14x+32.

$$x^{2}=280476x^{2}+641088x$$

Tangohia te 280476x^{2} mai i ngā taha e rua.

$$x^{2}-280476x^{2}=641088x$$

Pahekotia te x^{2} me -280476x^{2}, ka -280475x^{2}.

$$-280475x^{2}=641088x$$

Tangohia te 641088x mai i ngā taha e rua.

$$-280475x^{2}-641088x=0$$

Whakawehea ngā taha e rua ki te -280475.

$$\frac{-280475x^{2}-641088x}{-280475}=\frac{0}{-280475}$$

Mā te whakawehe ki te -280475 ka wetekia te whakareanga ki te -280475.

$$x^{2}+\left(-\frac{641088}{-280475}\right)x=\frac{0}{-280475}$$

Whakawehe -641088 ki te -280475.

$$x^{2}+\frac{641088}{280475}x=\frac{0}{-280475}$$

Whakawehe 0 ki te -280475.

$$x^{2}+\frac{641088}{280475}x=0$$

Whakawehea te \frac{641088}{280475}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{320544}{280475}. Nā, tāpiria te pūrua o te \frac{320544}{280475} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{641088}{280475}x+\left(\frac{320544}{280475}\right)^{2}=\left(\frac{320544}{280475}\right)^{2}$$

Pūruatia \frac{320544}{280475} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{641088}{280475}x+\frac{102748455936}{78666225625}=\frac{102748455936}{78666225625}$$

Tauwehea x^{2}+\frac{641088}{280475}x+\frac{102748455936}{78666225625}. 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}.

$$\left(x+\frac{320544}{280475}\right)^{2}=\frac{102748455936}{78666225625}$$

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

$$\sqrt{\left(x+\frac{320544}{280475}\right)^{2}}=\sqrt{\frac{102748455936}{78666225625}}$$

Whakarūnātia.

$$x+\frac{320544}{280475}=\frac{320544}{280475} x+\frac{320544}{280475}=-\frac{320544}{280475}$$

Me tango \frac{320544}{280475} mai i ngā taha e rua o te whārite.

$$x=0 x=-\frac{641088}{280475}$$