Whakaoti i te 4x(x+8)=6(x+8)

$$4x(x+8)=6(x+8)$$

Whakaoti mō x

$$x=-8$$

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 4x ki te x+8.

$$4x^{2}+32x=6\left(x+8\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6 ki te x+8.

$$4x^{2}+32x=6x+48$$

Tangohia te 6x mai i ngā taha e rua.

$$4x^{2}+32x-6x=48$$

Pahekotia te 32x me -6x, ka 26x.

$$4x^{2}+26x=48$$

Tangohia te 48 mai i ngā taha e rua.

$$4x^{2}+26x-48=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, 26 mō b, me -48 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-26±\sqrt{26^{2}-4\times 4\left(-48\right)}}{2\times 4}$$

Pūrua 26.

$$x=\frac{-26±\sqrt{676-4\times 4\left(-48\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{-26±\sqrt{676-16\left(-48\right)}}{2\times 4}$$

Whakareatia -16 ki te -48.

$$x=\frac{-26±\sqrt{676+768}}{2\times 4}$$

Tāpiri 676 ki te 768.

$$x=\frac{-26±\sqrt{1444}}{2\times 4}$$

Tuhia te pūtakerua o te 1444.

$$x=\frac{-26±38}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{-26±38}{8}$$

Nā, me whakaoti te whārite x=\frac{-26±38}{8} ina he tāpiri te ±. Tāpiri -26 ki te 38.

$$x=\frac{12}{8}$$

Whakahekea te hautanga \frac{12}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x=\frac{3}{2}$$

Nā, me whakaoti te whārite x=\frac{-26±38}{8} ina he tango te ±. Tango 38 mai i -26.

$$x=-\frac{64}{8}$$

Whakawehe -64 ki te 8.

$$x=-8$$

Kua oti te whārite te whakatau.

$$x=\frac{3}{2} x=-8$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 4x ki te x+8.

$$4x^{2}+32x=6\left(x+8\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6 ki te x+8.

$$4x^{2}+32x=6x+48$$

Tangohia te 6x mai i ngā taha e rua.

$$4x^{2}+32x-6x=48$$

Pahekotia te 32x me -6x, ka 26x.

$$4x^{2}+26x=48$$

Whakawehea ngā taha e rua ki te 4.

$$\frac{4x^{2}+26x}{4}=\frac{48}{4}$$

Mā te whakawehe ki te 4 ka wetekia te whakareanga ki te 4.

$$x^{2}+\frac{26}{4}x=\frac{48}{4}$$

Whakahekea te hautanga \frac{26}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}+\frac{13}{2}x=\frac{48}{4}$$

Whakawehe 48 ki te 4.

$$x^{2}+\frac{13}{2}x=12$$

Whakawehea te \frac{13}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{13}{4}. Nā, tāpiria te pūrua o te \frac{13}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{13}{2}x+\left(\frac{13}{4}\right)^{2}=12+\left(\frac{13}{4}\right)^{2}$$

Pūruatia \frac{13}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{13}{2}x+\frac{169}{16}=12+\frac{169}{16}$$

Tāpiri 12 ki te \frac{169}{16}.

$$x^{2}+\frac{13}{2}x+\frac{169}{16}=\frac{361}{16}$$

Tauwehea x^{2}+\frac{13}{2}x+\frac{169}{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}.

$$\left(x+\frac{13}{4}\right)^{2}=\frac{361}{16}$$

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

$$\sqrt{\left(x+\frac{13}{4}\right)^{2}}=\sqrt{\frac{361}{16}}$$

Whakarūnātia.

$$x+\frac{13}{4}=\frac{19}{4} x+\frac{13}{4}=-\frac{19}{4}$$

Me tango \frac{13}{4} mai i ngā taha e rua o te whārite.

$$x=\frac{3}{2} x=-8$$