Whakaoti i te 5-2x(x-1)=4(3-x)-2x

$$5-2x(x-1)=4(3-x)-2x$$

Whakaoti mō x

$$x=\frac{\sqrt{2}}{2}+2\approx 2.707106781$$

$$x=-\frac{\sqrt{2}}{2}+2\approx 1.292893219$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$5-2x\left(x-1\right)=12-4x-2x$$

Pahekotia te -4x me -2x, ka -6x.

$$5-2x\left(x-1\right)=12-6x$$

Tangohia te 12 mai i ngā taha e rua.

$$5-2x\left(x-1\right)-12=-6x$$

Me tāpiri te 6x ki ngā taha e rua.

$$5-2x\left(x-1\right)-12+6x=0$$

Me tāpiri te 12 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$5-2x\left(x-1\right)+6x=12$$

Tangohia te 12 mai i ngā taha e rua.

$$5-2x\left(x-1\right)+6x-12=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te -2x ki te x-1.

$$5-2x^{2}+2x+6x-12=0$$

Pahekotia te 2x me 6x, ka 8x.

$$5-2x^{2}+8x-12=0$$

Tangohia te 12 i te 5, ka -7.

$$-7-2x^{2}+8x=0$$

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.

$$-2x^{2}+8x-7=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -2 mō a, 8 mō b, me -7 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-2\right)\left(-7\right)}}{2\left(-2\right)}$$

Pūrua 8.

$$x=\frac{-8±\sqrt{64-4\left(-2\right)\left(-7\right)}}{2\left(-2\right)}$$

Whakareatia -4 ki te -2.

$$x=\frac{-8±\sqrt{64+8\left(-7\right)}}{2\left(-2\right)}$$

Whakareatia 8 ki te -7.

$$x=\frac{-8±\sqrt{64-56}}{2\left(-2\right)}$$

Tāpiri 64 ki te -56.

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

Tuhia te pūtakerua o te 8.

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

Whakareatia 2 ki te -2.

$$x=\frac{-8±2\sqrt{2}}{-4}$$

Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{2}}{-4} ina he tāpiri te ±. Tāpiri -8 ki te 2\sqrt{2}.

$$x=\frac{2\sqrt{2}-8}{-4}$$

Whakawehe 2\sqrt{2}-8 ki te -4.

$$x=-\frac{\sqrt{2}}{2}+2$$

Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{2}}{-4} ina he tango te ±. Tango 2\sqrt{2} mai i -8.

$$x=\frac{-2\sqrt{2}-8}{-4}$$

Whakawehe -8-2\sqrt{2} ki te -4.

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

Kua oti te whārite te whakatau.

$$x=-\frac{\sqrt{2}}{2}+2 x=\frac{\sqrt{2}}{2}+2$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$5-2x\left(x-1\right)=12-4x-2x$$

Pahekotia te -4x me -2x, ka -6x.

$$5-2x\left(x-1\right)=12-6x$$

Me tāpiri te 6x ki ngā taha e rua.

$$5-2x\left(x-1\right)+6x=12$$

Whakamahia te āhuatanga tohatoha hei whakarea te -2x ki te x-1.

$$5-2x^{2}+2x+6x=12$$

Pahekotia te 2x me 6x, ka 8x.

$$5-2x^{2}+8x=12$$

Tangohia te 5 mai i ngā taha e rua.

$$-2x^{2}+8x=12-5$$

Tangohia te 5 i te 12, ka 7.

$$-2x^{2}+8x=7$$

Whakawehea ngā taha e rua ki te -2.

$$\frac{-2x^{2}+8x}{-2}=\frac{7}{-2}$$

Mā te whakawehe ki te -2 ka wetekia te whakareanga ki te -2.

$$x^{2}+\frac{8}{-2}x=\frac{7}{-2}$$

Whakawehe 8 ki te -2.

$$x^{2}-4x=\frac{7}{-2}$$

Whakawehe 7 ki te -2.

$$x^{2}-4x=-\frac{7}{2}$$

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

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

Pūrua -2.

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

Tāpiri -\frac{7}{2} ki te 4.

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

Tauwehea x^{2}-4x+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}.

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

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

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{\frac{1}{2}}$$

Whakarūnātia.

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

Me tāpiri 2 ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{2}}{2}+2 x=-\frac{\sqrt{2}}{2}+2$$