Whakaoti i te (x+2)(x-6)=3

$$( x + 2 ) ( x - 6 ) = 3$$

Whakaoti mō x

$$x=\sqrt{19}+2\approx 6.358898944$$

$$x=2-\sqrt{19}\approx -2.358898944$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x+2 ki te x-6 ka whakakotahi i ngā kupu rite.

$$x^{2}-4x-12=3$$

Tangohia te 3 mai i ngā taha e rua.

$$x^{2}-4x-12-3=0$$

Tangohia te 3 i te -12, ka -15.

$$x^{2}-4x-15=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -4 mō b, me -15 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\left(-15\right)}}{2}$$

Pūrua -4.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\left(-15\right)}}{2}$$

Whakareatia -4 ki te -15.

$$x=\frac{-\left(-4\right)±\sqrt{16+60}}{2}$$

Tāpiri 16 ki te 60.

$$x=\frac{-\left(-4\right)±\sqrt{76}}{2}$$

Tuhia te pūtakerua o te 76.

$$x=\frac{-\left(-4\right)±2\sqrt{19}}{2}$$

Ko te tauaro o -4 ko 4.

$$x=\frac{4±2\sqrt{19}}{2}$$

Nā, me whakaoti te whārite x=\frac{4±2\sqrt{19}}{2} ina he tāpiri te ±. Tāpiri 4 ki te 2\sqrt{19}.

$$x=\frac{2\sqrt{19}+4}{2}$$

Whakawehe 4+2\sqrt{19} ki te 2.

$$x=\sqrt{19}+2$$

Nā, me whakaoti te whārite x=\frac{4±2\sqrt{19}}{2} ina he tango te ±. Tango 2\sqrt{19} mai i 4.

$$x=\frac{4-2\sqrt{19}}{2}$$

Whakawehe 4-2\sqrt{19} ki te 2.

$$x=2-\sqrt{19}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{19}+2 x=2-\sqrt{19}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x+2 ki te x-6 ka whakakotahi i ngā kupu rite.

$$x^{2}-4x-12=3$$

Me tāpiri te 12 ki ngā taha e rua.

$$x^{2}-4x=3+12$$

Tāpirihia te 3 ki te 12, ka 15.

$$x^{2}-4x=15$$

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.

$$x^{2}-4x+\left(-2\right)^{2}=15+\left(-2\right)^{2}$$

Pūrua -2.

$$x^{2}-4x+4=15+4$$

Tāpiri 15 ki te 4.

$$x^{2}-4x+4=19$$

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}.

$$\left(x-2\right)^{2}=19$$

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

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{19}$$

Whakarūnātia.

$$x-2=\sqrt{19} x-2=-\sqrt{19}$$

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

$$x=\sqrt{19}+2 x=2-\sqrt{19}$$