Whakaoti i te (x-4)*(x+3)=x

$$( x - 4 ) \cdot ( x + 3 ) = x$$

Whakaoti mō x

$$x=\sqrt{13}+1\approx 4.605551275$$

$$x=1-\sqrt{13}\approx -2.605551275$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x-4 ki te x+3 ka whakakotahi i ngā kupu rite.

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

Tangohia te x mai i ngā taha e rua.

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

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

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

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

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

Pūrua -2.

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

Whakareatia -4 ki te -12.

$$x=\frac{-\left(-2\right)±\sqrt{4+48}}{2}$$

Tāpiri 4 ki te 48.

$$x=\frac{-\left(-2\right)±\sqrt{52}}{2}$$

Tuhia te pūtakerua o te 52.

$$x=\frac{-\left(-2\right)±2\sqrt{13}}{2}$$

Ko te tauaro o -2 ko 2.

$$x=\frac{2±2\sqrt{13}}{2}$$

Nā, me whakaoti te whārite x=\frac{2±2\sqrt{13}}{2} ina he tāpiri te ±. Tāpiri 2 ki te 2\sqrt{13}.

$$x=\frac{2\sqrt{13}+2}{2}$$

Whakawehe 2+2\sqrt{13} ki te 2.

$$x=\sqrt{13}+1$$

Nā, me whakaoti te whārite x=\frac{2±2\sqrt{13}}{2} ina he tango te ±. Tango 2\sqrt{13} mai i 2.

$$x=\frac{2-2\sqrt{13}}{2}$$

Whakawehe 2-2\sqrt{13} ki te 2.

$$x=1-\sqrt{13}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{13}+1 x=1-\sqrt{13}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x-4 ki te x+3 ka whakakotahi i ngā kupu rite.

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

Tangohia te x mai i ngā taha e rua.

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

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

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

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

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

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

$$x^{2}-2x+1=12+1$$

Tāpiri 12 ki te 1.

$$x^{2}-2x+1=13$$

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

$$\left(x-1\right)^{2}=13$$

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

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{13}$$

Whakarūnātia.

$$x-1=\sqrt{13} x-1=-\sqrt{13}$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$x=\sqrt{13}+1 x=1-\sqrt{13}$$