Whakaoti i te 2x-7/x+3=7

$$2 x - \frac { 7 } { x + 3 } = 7$$

Whakaoti mō x

$$x = -\frac{7}{2} = -3\frac{1}{2} = -3.5$$

$$x=4$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki -3 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x+3.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te x+3.

$$2x^{2}+6x-7=7\left(x+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 7 ki te x+3.

$$2x^{2}+6x-7=7x+21$$

Tangohia te 7x mai i ngā taha e rua.

$$2x^{2}+6x-7-7x=21$$

Pahekotia te 6x me -7x, ka -x.

$$2x^{2}-x-7=21$$

Tangohia te 21 mai i ngā taha e rua.

$$2x^{2}-x-7-21=0$$

Tangohia te 21 i te -7, ka -28.

$$2x^{2}-x-28=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, -1 mō b, me -28 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\times 2\left(-28\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-\left(-1\right)±\sqrt{1-8\left(-28\right)}}{2\times 2}$$

Whakareatia -8 ki te -28.

$$x=\frac{-\left(-1\right)±\sqrt{1+224}}{2\times 2}$$

Tāpiri 1 ki te 224.

$$x=\frac{-\left(-1\right)±\sqrt{225}}{2\times 2}$$

Tuhia te pūtakerua o te 225.

$$x=\frac{-\left(-1\right)±15}{2\times 2}$$

Ko te tauaro o -1 ko 1.

$$x=\frac{1±15}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{1±15}{4}$$

Nā, me whakaoti te whārite x=\frac{1±15}{4} ina he tāpiri te ±. Tāpiri 1 ki te 15.

$$x=\frac{16}{4}$$

Whakawehe 16 ki te 4.

$$x=4$$

Nā, me whakaoti te whārite x=\frac{1±15}{4} ina he tango te ±. Tango 15 mai i 1.

$$x=-\frac{14}{4}$$

Whakahekea te hautanga \frac{-14}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

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

Kua oti te whārite te whakatau.

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

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki -3 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x+3.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te x+3.

$$2x^{2}+6x-7=7\left(x+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 7 ki te x+3.

$$2x^{2}+6x-7=7x+21$$

Tangohia te 7x mai i ngā taha e rua.

$$2x^{2}+6x-7-7x=21$$

Pahekotia te 6x me -7x, ka -x.

$$2x^{2}-x-7=21$$

Me tāpiri te 7 ki ngā taha e rua.

$$2x^{2}-x=21+7$$

Tāpirihia te 21 ki te 7, ka 28.

$$2x^{2}-x=28$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}-x}{2}=\frac{28}{2}$$

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

$$x^{2}-\frac{1}{2}x=\frac{28}{2}$$

Whakawehe 28 ki te 2.

$$x^{2}-\frac{1}{2}x=14$$

Whakawehea te -\frac{1}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{4}. Nā, tāpiria te pūrua o te -\frac{1}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{1}{2}x+\left(-\frac{1}{4}\right)^{2}=14+\left(-\frac{1}{4}\right)^{2}$$

Pūruatia -\frac{1}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{1}{2}x+\frac{1}{16}=14+\frac{1}{16}$$

Tāpiri 14 ki te \frac{1}{16}.

$$x^{2}-\frac{1}{2}x+\frac{1}{16}=\frac{225}{16}$$

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

$$\left(x-\frac{1}{4}\right)^{2}=\frac{225}{16}$$

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

$$\sqrt{\left(x-\frac{1}{4}\right)^{2}}=\sqrt{\frac{225}{16}}$$

Whakarūnātia.

$$x-\frac{1}{4}=\frac{15}{4} x-\frac{1}{4}=-\frac{15}{4}$$

Me tāpiri \frac{1}{4} ki ngā taha e rua o te whārite.

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