Whakaoti i te x(x+1)*8=96

$$x ( x + 1 ) \times 8 = 96$$

Whakaoti mō x

$$x=3$$

$$x=-4$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x+1.

$$\left(x^{2}+x\right)\times 8=96$$

Whakamahia te āhuatanga tohatoha hei whakarea te x^{2}+x ki te 8.

$$8x^{2}+8x=96$$

Tangohia te 96 mai i ngā taha e rua.

$$8x^{2}+8x-96=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 8 mō a, 8 mō b, me -96 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\times 8\left(-96\right)}}{2\times 8}$$

Pūrua 8.

$$x=\frac{-8±\sqrt{64-4\times 8\left(-96\right)}}{2\times 8}$$

Whakareatia -4 ki te 8.

$$x=\frac{-8±\sqrt{64-32\left(-96\right)}}{2\times 8}$$

Whakareatia -32 ki te -96.

$$x=\frac{-8±\sqrt{64+3072}}{2\times 8}$$

Tāpiri 64 ki te 3072.

$$x=\frac{-8±\sqrt{3136}}{2\times 8}$$

Tuhia te pūtakerua o te 3136.

$$x=\frac{-8±56}{2\times 8}$$

Whakareatia 2 ki te 8.

$$x=\frac{-8±56}{16}$$

Nā, me whakaoti te whārite x=\frac{-8±56}{16} ina he tāpiri te ±. Tāpiri -8 ki te 56.

$$x=\frac{48}{16}$$

Whakawehe 48 ki te 16.

$$x=3$$

Nā, me whakaoti te whārite x=\frac{-8±56}{16} ina he tango te ±. Tango 56 mai i -8.

$$x=-\frac{64}{16}$$

Whakawehe -64 ki te 16.

$$x=-4$$

Kua oti te whārite te whakatau.

$$x=3 x=-4$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x+1.

$$\left(x^{2}+x\right)\times 8=96$$

Whakamahia te āhuatanga tohatoha hei whakarea te x^{2}+x ki te 8.

$$8x^{2}+8x=96$$

Whakawehea ngā taha e rua ki te 8.

$$\frac{8x^{2}+8x}{8}=\frac{96}{8}$$

Mā te whakawehe ki te 8 ka wetekia te whakareanga ki te 8.

$$x^{2}+\frac{8}{8}x=\frac{96}{8}$$

Whakawehe 8 ki te 8.

$$x^{2}+x=\frac{96}{8}$$

Whakawehe 96 ki te 8.

$$x^{2}+x=12$$

Whakawehea te 1, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1}{2}. Nā, tāpiria te pūrua o te \frac{1}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+x+\left(\frac{1}{2}\right)^{2}=12+\left(\frac{1}{2}\right)^{2}$$

Pūruatia \frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+x+\frac{1}{4}=12+\frac{1}{4}$$

Tāpiri 12 ki te \frac{1}{4}.

$$x^{2}+x+\frac{1}{4}=\frac{49}{4}$$

Tauwehea x^{2}+x+\frac{1}{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}.

$$\left(x+\frac{1}{2}\right)^{2}=\frac{49}{4}$$

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

$$\sqrt{\left(x+\frac{1}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Whakarūnātia.

$$x+\frac{1}{2}=\frac{7}{2} x+\frac{1}{2}=-\frac{7}{2}$$

Me tango \frac{1}{2} mai i ngā taha e rua o te whārite.

$$x=3 x=-4$$