Whakaoti i te (x-6)^2=2x^2-15x+38

$$( x - 6 ) ^ { 2 } = 2 x ^ { 2 } - 15 x + 38$$

Whakaoti mō x

$$x=1$$

$$x=2$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-6\right)^{2}.

$$x^{2}-12x+36=2x^{2}-15x+38$$

Tangohia te 2x^{2} mai i ngā taha e rua.

$$x^{2}-12x+36-2x^{2}=-15x+38$$

Pahekotia te x^{2} me -2x^{2}, ka -x^{2}.

$$-x^{2}-12x+36=-15x+38$$

Me tāpiri te 15x ki ngā taha e rua.

$$-x^{2}-12x+36+15x=38$$

Pahekotia te -12x me 15x, ka 3x.

$$-x^{2}+3x+36=38$$

Tangohia te 38 mai i ngā taha e rua.

$$-x^{2}+3x+36-38=0$$

Tangohia te 38 i te 36, ka -2.

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

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx-2. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=3 ab=-\left(-2\right)=2$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=2 b=1$$

Tuhia anō te -x^{2}+3x-2 hei \left(-x^{2}+2x\right)+\left(x-2\right).

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

Whakatauwehea atu -x i te -x^{2}+2x.

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

Whakatauwehea atu te kīanga pātahi x-2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-2\right)\left(-x+1\right)$$

Hei kimi otinga whārite, me whakaoti te x-2=0 me te -x+1=0.

$$x=2 x=1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-6\right)^{2}.

$$x^{2}-12x+36=2x^{2}-15x+38$$

Tangohia te 2x^{2} mai i ngā taha e rua.

$$x^{2}-12x+36-2x^{2}=-15x+38$$

Pahekotia te x^{2} me -2x^{2}, ka -x^{2}.

$$-x^{2}-12x+36=-15x+38$$

Me tāpiri te 15x ki ngā taha e rua.

$$-x^{2}-12x+36+15x=38$$

Pahekotia te -12x me 15x, ka 3x.

$$-x^{2}+3x+36=38$$

Tangohia te 38 mai i ngā taha e rua.

$$-x^{2}+3x+36-38=0$$

Tangohia te 38 i te 36, ka -2.

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

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

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

Pūrua 3.

$$x=\frac{-3±\sqrt{9-4\left(-1\right)\left(-2\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-3±\sqrt{9+4\left(-2\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -2.

$$x=\frac{-3±\sqrt{9-8}}{2\left(-1\right)}$$

Tāpiri 9 ki te -8.

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

Tuhia te pūtakerua o te 1.

$$x=\frac{-3±1}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-3±1}{-2}$$

Nā, me whakaoti te whārite x=\frac{-3±1}{-2} ina he tāpiri te ±. Tāpiri -3 ki te 1.

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

Whakawehe -2 ki te -2.

$$x=1$$

Nā, me whakaoti te whārite x=\frac{-3±1}{-2} ina he tango te ±. Tango 1 mai i -3.

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

Whakawehe -4 ki te -2.

$$x=2$$

Kua oti te whārite te whakatau.

$$x=1 x=2$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-6\right)^{2}.

$$x^{2}-12x+36=2x^{2}-15x+38$$

Tangohia te 2x^{2} mai i ngā taha e rua.

$$x^{2}-12x+36-2x^{2}=-15x+38$$

Pahekotia te x^{2} me -2x^{2}, ka -x^{2}.

$$-x^{2}-12x+36=-15x+38$$

Me tāpiri te 15x ki ngā taha e rua.

$$-x^{2}-12x+36+15x=38$$

Pahekotia te -12x me 15x, ka 3x.

$$-x^{2}+3x+36=38$$

Tangohia te 36 mai i ngā taha e rua.

$$-x^{2}+3x=38-36$$

Tangohia te 36 i te 38, ka 2.

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

Whakawehea ngā taha e rua ki te -1.

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

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

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

Whakawehe 3 ki te -1.

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

Whakawehe 2 ki te -1.

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

Whakawehea te -3, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{3}{2}. Nā, tāpiria te pūrua o te -\frac{3}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

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

Pūruatia -\frac{3}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-3x+\frac{9}{4}=-2+\frac{9}{4}$$

Tāpiri -2 ki te \frac{9}{4}.

$$x^{2}-3x+\frac{9}{4}=\frac{1}{4}$$

Tauwehea x^{2}-3x+\frac{9}{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}.

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

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

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

Whakarūnātia.

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

Me tāpiri \frac{3}{2} ki ngā taha e rua o te whārite.

$$x=2 x=1$$