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

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

Whakaoti mō x

$$x=\sqrt{6}\approx 2.449489743$$

$$x=-\sqrt{6}\approx -2.449489743$$

Ngā Upane mā te Kimi Pūtakerua

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

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

Me tāpiri te x ki ngā taha e rua.

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

Pahekotia te -x me x, ka 0.

$$x^{2}-6=0$$

Me tāpiri te 6 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$x^{2}=6$$

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

$$x=\sqrt{6} x=-\sqrt{6}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

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

Me tāpiri te x ki ngā taha e rua.

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

Pahekotia te -x me x, ka 0.

$$x^{2}-6=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -6 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-6\right)}}{2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-6\right)}}{2}$$

Whakareatia -4 ki te -6.

$$x=\frac{0±\sqrt{24}}{2}$$

Tuhia te pūtakerua o te 24.

$$x=\frac{0±2\sqrt{6}}{2}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{6}}{2} ina he tāpiri te ±.

$$x=\sqrt{6}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{6}}{2} ina he tango te ±.

$$x=-\sqrt{6}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{6} x=-\sqrt{6}$$