Whakaoti i te x^2+(6-3x)^2+4x+16(6-3x)+28=0

$$x ^ { 2 } + ( 6 - 3 x ) ^ { 2 } + 4 x + 16 ( 6 - 3 x ) + 28 = 0$$

Whakaoti mō x

$$x=4$$

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(6-3x\right)^{2}.

$$x^{2}+36-36x+9x^{2}+4x+16\left(6-3x\right)+28=0$$

Pahekotia te x^{2} me 9x^{2}, ka 10x^{2}.

$$10x^{2}+36-36x+4x+16\left(6-3x\right)+28=0$$

Pahekotia te -36x me 4x, ka -32x.

$$10x^{2}+36-32x+16\left(6-3x\right)+28=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 16 ki te 6-3x.

$$10x^{2}+36-32x+96-48x+28=0$$

Tāpirihia te 36 ki te 96, ka 132.

$$10x^{2}+132-32x-48x+28=0$$

Pahekotia te -32x me -48x, ka -80x.

$$10x^{2}+132-80x+28=0$$

Tāpirihia te 132 ki te 28, ka 160.

$$10x^{2}+160-80x=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$10x^{2}-80x+160=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 10 mō a, -80 mō b, me 160 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-80\right)±\sqrt{\left(-80\right)^{2}-4\times 10\times 160}}{2\times 10}$$

Pūrua -80.

$$x=\frac{-\left(-80\right)±\sqrt{6400-4\times 10\times 160}}{2\times 10}$$

Whakareatia -4 ki te 10.

$$x=\frac{-\left(-80\right)±\sqrt{6400-40\times 160}}{2\times 10}$$

Whakareatia -40 ki te 160.

$$x=\frac{-\left(-80\right)±\sqrt{6400-6400}}{2\times 10}$$

Tāpiri 6400 ki te -6400.

$$x=\frac{-\left(-80\right)±\sqrt{0}}{2\times 10}$$

Tuhia te pūtakerua o te 0.

$$x=-\frac{-80}{2\times 10}$$

Ko te tauaro o -80 ko 80.

$$x=\frac{80}{2\times 10}$$

Whakareatia 2 ki te 10.

$$x=\frac{80}{20}$$

Whakawehe 80 ki te 20.

$$x=4$$

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(6-3x\right)^{2}.

$$x^{2}+36-36x+9x^{2}+4x+16\left(6-3x\right)+28=0$$

Pahekotia te x^{2} me 9x^{2}, ka 10x^{2}.

$$10x^{2}+36-36x+4x+16\left(6-3x\right)+28=0$$

Pahekotia te -36x me 4x, ka -32x.

$$10x^{2}+36-32x+16\left(6-3x\right)+28=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 16 ki te 6-3x.

$$10x^{2}+36-32x+96-48x+28=0$$

Tāpirihia te 36 ki te 96, ka 132.

$$10x^{2}+132-32x-48x+28=0$$

Pahekotia te -32x me -48x, ka -80x.

$$10x^{2}+132-80x+28=0$$

Tāpirihia te 132 ki te 28, ka 160.

$$10x^{2}+160-80x=0$$

Tangohia te 160 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$10x^{2}-80x=-160$$

Whakawehea ngā taha e rua ki te 10.

$$\frac{10x^{2}-80x}{10}=-\frac{160}{10}$$

Mā te whakawehe ki te 10 ka wetekia te whakareanga ki te 10.

$$x^{2}+\left(-\frac{80}{10}\right)x=-\frac{160}{10}$$

Whakawehe -80 ki te 10.

$$x^{2}-8x=-\frac{160}{10}$$

Whakawehe -160 ki te 10.

$$x^{2}-8x=-16$$

Whakawehea te -8, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -4. Nā, tāpiria te pūrua o te -4 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-8x+\left(-4\right)^{2}=-16+\left(-4\right)^{2}$$

Pūrua -4.

$$x^{2}-8x+16=-16+16$$

Tāpiri -16 ki te 16.

$$x^{2}-8x+16=0$$

Tauwehea x^{2}-8x+16. 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}.

$$\left(x-4\right)^{2}=0$$

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

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

Whakarūnātia.

$$x-4=0 x-4=0$$

Me tāpiri 4 ki ngā taha e rua o te whārite.

$$x=4 x=4$$

Kua oti te whārite te whakatau. He ōrite ngā whakatau.

$$x=4$$