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

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

Whakaoti mō x

$$x=1$$

$$x=7$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 2x-5 ki te x-4 ka whakakotahi i ngā kupu rite.

$$2x^{2}-13x+20-7=\left(x-2\right)\left(x-3\right)$$

Tangohia te 7 i te 20, ka 13.

$$2x^{2}-13x+13=\left(x-2\right)\left(x-3\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-2 ki te x-3 ka whakakotahi i ngā kupu rite.

$$2x^{2}-13x+13=x^{2}-5x+6$$

Tangohia te x^{2} mai i ngā taha e rua.

$$2x^{2}-13x+13-x^{2}=-5x+6$$

Pahekotia te 2x^{2} me -x^{2}, ka x^{2}.

$$x^{2}-13x+13=-5x+6$$

Me tāpiri te 5x ki ngā taha e rua.

$$x^{2}-13x+13+5x=6$$

Pahekotia te -13x me 5x, ka -8x.

$$x^{2}-8x+13=6$$

Tangohia te 6 mai i ngā taha e rua.

$$x^{2}-8x+13-6=0$$

Tangohia te 6 i te 13, ka 7.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -8 mō b, me 7 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Pūrua -8.

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

Whakareatia -4 ki te 7.

$$x=\frac{-\left(-8\right)±\sqrt{64-28}}{2}$$

Tāpiri 64 ki te -28.

$$x=\frac{-\left(-8\right)±\sqrt{36}}{2}$$

Tuhia te pūtakerua o te 36.

$$x=\frac{-\left(-8\right)±6}{2}$$

Ko te tauaro o -8 ko 8.

$$x=\frac{8±6}{2}$$

Nā, me whakaoti te whārite x=\frac{8±6}{2} ina he tāpiri te ±. Tāpiri 8 ki te 6.

$$x=\frac{14}{2}$$

Whakawehe 14 ki te 2.

$$x=7$$

Nā, me whakaoti te whārite x=\frac{8±6}{2} ina he tango te ±. Tango 6 mai i 8.

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

Whakawehe 2 ki te 2.

$$x=1$$

Kua oti te whārite te whakatau.

$$x=7 x=1$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 2x-5 ki te x-4 ka whakakotahi i ngā kupu rite.

$$2x^{2}-13x+20-7=\left(x-2\right)\left(x-3\right)$$

Tangohia te 7 i te 20, ka 13.

$$2x^{2}-13x+13=\left(x-2\right)\left(x-3\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-2 ki te x-3 ka whakakotahi i ngā kupu rite.

$$2x^{2}-13x+13=x^{2}-5x+6$$

Tangohia te x^{2} mai i ngā taha e rua.

$$2x^{2}-13x+13-x^{2}=-5x+6$$

Pahekotia te 2x^{2} me -x^{2}, ka x^{2}.

$$x^{2}-13x+13=-5x+6$$

Me tāpiri te 5x ki ngā taha e rua.

$$x^{2}-13x+13+5x=6$$

Pahekotia te -13x me 5x, ka -8x.

$$x^{2}-8x+13=6$$

Tangohia te 13 mai i ngā taha e rua.

$$x^{2}-8x=6-13$$

Tangohia te 13 i te 6, ka -7.

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

Whakawehea te -8, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -4. Nā, tāpiria te pūrua o te -4 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

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

Pūrua -4.

$$x^{2}-8x+16=-7+16$$

Tāpiri -7 ki te 16.

$$x^{2}-8x+16=9$$

Tauwehea x^{2}-8x+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}.

$$\left(x-4\right)^{2}=9$$

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

$$\sqrt{\left(x-4\right)^{2}}=\sqrt{9}$$

Whakarūnātia.

$$x-4=3 x-4=-3$$

Me tāpiri 4 ki ngā taha e rua o te whārite.

$$x=7 x=1$$