Whakaoti i te -x(x+2)+3=0

$$-x(x+2)+3=0$$

Whakaoti mō x

$$x=-3$$

$$x=1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$\left(-x\right)x+2\left(-x\right)+3=0$$

Whakareatia te x ki te x, ka x^{2}.

$$-x^{2}+2\left(-1\right)x+3=0$$

Whakareatia te 2 ki te -1, ka -2.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, -2 mō b, me 3 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-1\right)\times 3}}{2\left(-1\right)}$$

Pūrua -2.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\left(-1\right)\times 3}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-\left(-2\right)±\sqrt{4+4\times 3}}{2\left(-1\right)}$$

Whakareatia 4 ki te 3.

$$x=\frac{-\left(-2\right)±\sqrt{4+12}}{2\left(-1\right)}$$

Tāpiri 4 ki te 12.

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

Tuhia te pūtakerua o te 16.

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

Ko te tauaro o -2 ko 2.

$$x=\frac{2±4}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{2±4}{-2}$$

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

$$x=\frac{6}{-2}$$

Whakawehe 6 ki te -2.

$$x=-3$$

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

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

Whakawehe -2 ki te -2.

$$x=1$$

Kua oti te whārite te whakatau.

$$x=-3 x=1$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$\left(-x\right)x+2\left(-x\right)+3=0$$

Tangohia te 3 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

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

Whakareatia te x ki te x, ka x^{2}.

$$-x^{2}+2\left(-1\right)x=-3$$

Whakareatia te 2 ki te -1, ka -2.

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

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}-2x}{-1}=-\frac{3}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$x^{2}+\left(-\frac{2}{-1}\right)x=-\frac{3}{-1}$$

Whakawehe -2 ki te -1.

$$x^{2}+2x=-\frac{3}{-1}$$

Whakawehe -3 ki te -1.

$$x^{2}+2x=3$$

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.

$$x^{2}+2x+1^{2}=3+1^{2}$$

Pūrua 1.

$$x^{2}+2x+1=3+1$$

Tāpiri 3 ki te 1.

$$x^{2}+2x+1=4$$

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}.

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

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

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{4}$$

Whakarūnātia.

$$x+1=2 x+1=-2$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$x=1 x=-3$$