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

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

Whakaoti mō x

$$x=4$$

$$x=8$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x-7 ki te x-5 ka whakakotahi i ngā kupu rite.

$$x^{2}-12x+35=3$$

Tangohia te 3 mai i ngā taha e rua.

$$x^{2}-12x+35-3=0$$

Tangohia te 3 i te 35, ka 32.

$$x^{2}-12x+32=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -12 mō b, me 32 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 32}}{2}$$

Pūrua -12.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\times 32}}{2}$$

Whakareatia -4 ki te 32.

$$x=\frac{-\left(-12\right)±\sqrt{144-128}}{2}$$

Tāpiri 144 ki te -128.

$$x=\frac{-\left(-12\right)±\sqrt{16}}{2}$$

Tuhia te pūtakerua o te 16.

$$x=\frac{-\left(-12\right)±4}{2}$$

Ko te tauaro o -12 ko 12.

$$x=\frac{12±4}{2}$$

Nā, me whakaoti te whārite x=\frac{12±4}{2} ina he tāpiri te ±. Tāpiri 12 ki te 4.

$$x=\frac{16}{2}$$

Whakawehe 16 ki te 2.

$$x=8$$

Nā, me whakaoti te whārite x=\frac{12±4}{2} ina he tango te ±. Tango 4 mai i 12.

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

Whakawehe 8 ki te 2.

$$x=4$$

Kua oti te whārite te whakatau.

$$x=8 x=4$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x-7 ki te x-5 ka whakakotahi i ngā kupu rite.

$$x^{2}-12x+35=3$$

Tangohia te 35 mai i ngā taha e rua.

$$x^{2}-12x=3-35$$

Tangohia te 35 i te 3, ka -32.

$$x^{2}-12x=-32$$

Whakawehea te -12, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -6. Nā, tāpiria te pūrua o te -6 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-12x+\left(-6\right)^{2}=-32+\left(-6\right)^{2}$$

Pūrua -6.

$$x^{2}-12x+36=-32+36$$

Tāpiri -32 ki te 36.

$$x^{2}-12x+36=4$$

Tauwehea x^{2}-12x+36. 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}.

$$\left(x-6\right)^{2}=4$$

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

$$\sqrt{\left(x-6\right)^{2}}=\sqrt{4}$$

Whakarūnātia.

$$x-6=2 x-6=-2$$

Me tāpiri 6 ki ngā taha e rua o te whārite.

$$x=8 x=4$$