Whakaoti i te -(3x-4)4(x-5)=2(7-4x)

$$-(3x-4)4(x-5)=2(7-4x)$$

Whakaoti mō x

$$x=\frac{\sqrt{159}}{6}+\frac{7}{2}\approx 5.601586702$$

$$x=-\frac{\sqrt{159}}{6}+\frac{7}{2}\approx 1.398413298$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Hei kimi i te tauaro o 3x-4, kimihia te tauaro o ia taurangi.

$$\left(-3x-\left(-4\right)\right)\times 4\left(x-5\right)=2\left(7-4x\right)$$

Ko te tauaro o -4 ko 4.

$$\left(-3x+4\right)\times 4\left(x-5\right)=2\left(7-4x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -3x+4 ki te 4.

$$\left(-12x+16\right)\left(x-5\right)=2\left(7-4x\right)$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o -12x+16 ki ia tau o x-5.

$$-12x^{2}+60x+16x-80=2\left(7-4x\right)$$

Pahekotia te 60x me 16x, ka 76x.

$$-12x^{2}+76x-80=2\left(7-4x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te 7-4x.

$$-12x^{2}+76x-80=14-8x$$

Tangohia te 14 mai i ngā taha e rua.

$$-12x^{2}+76x-80-14=-8x$$

Tangohia te 14 i te -80, ka -94.

$$-12x^{2}+76x-94=-8x$$

Me tāpiri te 8x ki ngā taha e rua.

$$-12x^{2}+76x-94+8x=0$$

Pahekotia te 76x me 8x, ka 84x.

$$-12x^{2}+84x-94=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -12 mō a, 84 mō b, me -94 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-84±\sqrt{84^{2}-4\left(-12\right)\left(-94\right)}}{2\left(-12\right)}$$

Pūrua 84.

$$x=\frac{-84±\sqrt{7056-4\left(-12\right)\left(-94\right)}}{2\left(-12\right)}$$

Whakareatia -4 ki te -12.

$$x=\frac{-84±\sqrt{7056+48\left(-94\right)}}{2\left(-12\right)}$$

Whakareatia 48 ki te -94.

$$x=\frac{-84±\sqrt{7056-4512}}{2\left(-12\right)}$$

Tāpiri 7056 ki te -4512.

$$x=\frac{-84±\sqrt{2544}}{2\left(-12\right)}$$

Tuhia te pūtakerua o te 2544.

$$x=\frac{-84±4\sqrt{159}}{2\left(-12\right)}$$

Whakareatia 2 ki te -12.

$$x=\frac{-84±4\sqrt{159}}{-24}$$

Nā, me whakaoti te whārite x=\frac{-84±4\sqrt{159}}{-24} ina he tāpiri te ±. Tāpiri -84 ki te 4\sqrt{159}.

$$x=\frac{4\sqrt{159}-84}{-24}$$

Whakawehe -84+4\sqrt{159} ki te -24.

$$x=-\frac{\sqrt{159}}{6}+\frac{7}{2}$$

Nā, me whakaoti te whārite x=\frac{-84±4\sqrt{159}}{-24} ina he tango te ±. Tango 4\sqrt{159} mai i -84.

$$x=\frac{-4\sqrt{159}-84}{-24}$$

Whakawehe -84-4\sqrt{159} ki te -24.

$$x=\frac{\sqrt{159}}{6}+\frac{7}{2}$$

Kua oti te whārite te whakatau.

$$x=-\frac{\sqrt{159}}{6}+\frac{7}{2} x=\frac{\sqrt{159}}{6}+\frac{7}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Hei kimi i te tauaro o 3x-4, kimihia te tauaro o ia taurangi.

$$\left(-3x-\left(-4\right)\right)\times 4\left(x-5\right)=2\left(7-4x\right)$$

Ko te tauaro o -4 ko 4.

$$\left(-3x+4\right)\times 4\left(x-5\right)=2\left(7-4x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -3x+4 ki te 4.

$$\left(-12x+16\right)\left(x-5\right)=2\left(7-4x\right)$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o -12x+16 ki ia tau o x-5.

$$-12x^{2}+60x+16x-80=2\left(7-4x\right)$$

Pahekotia te 60x me 16x, ka 76x.

$$-12x^{2}+76x-80=2\left(7-4x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te 7-4x.

$$-12x^{2}+76x-80=14-8x$$

Me tāpiri te 8x ki ngā taha e rua.

$$-12x^{2}+76x-80+8x=14$$

Pahekotia te 76x me 8x, ka 84x.

$$-12x^{2}+84x-80=14$$

Me tāpiri te 80 ki ngā taha e rua.

$$-12x^{2}+84x=14+80$$

Tāpirihia te 14 ki te 80, ka 94.

$$-12x^{2}+84x=94$$

Whakawehea ngā taha e rua ki te -12.

$$\frac{-12x^{2}+84x}{-12}=\frac{94}{-12}$$

Mā te whakawehe ki te -12 ka wetekia te whakareanga ki te -12.

$$x^{2}+\frac{84}{-12}x=\frac{94}{-12}$$

Whakawehe 84 ki te -12.

$$x^{2}-7x=\frac{94}{-12}$$

Whakahekea te hautanga \frac{94}{-12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}-7x=-\frac{47}{6}$$

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.

$$x^{2}-7x+\left(-\frac{7}{2}\right)^{2}=-\frac{47}{6}+\left(-\frac{7}{2}\right)^{2}$$

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

$$x^{2}-7x+\frac{49}{4}=-\frac{47}{6}+\frac{49}{4}$$

Tāpiri -\frac{47}{6} ki te \frac{49}{4} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}-7x+\frac{49}{4}=\frac{53}{12}$$

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}.

$$\left(x-\frac{7}{2}\right)^{2}=\frac{53}{12}$$

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

$$\sqrt{\left(x-\frac{7}{2}\right)^{2}}=\sqrt{\frac{53}{12}}$$

Whakarūnātia.

$$x-\frac{7}{2}=\frac{\sqrt{159}}{6} x-\frac{7}{2}=-\frac{\sqrt{159}}{6}$$

Me tāpiri \frac{7}{2} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{159}}{6}+\frac{7}{2} x=-\frac{\sqrt{159}}{6}+\frac{7}{2}$$