Whakaoti i te (x+2)^2/2+x^2-18/3=2x+2

$$\frac { ( x + 2 ) ^ { 2 } } { 2 } + \frac { x ^ { 2 } - 18 } { 3 } = 2 x + 2$$

Whakaoti mō x

$$x = \frac{6 \sqrt{5}}{5} \approx 2.683281573$$

$$x = -\frac{6 \sqrt{5}}{5} \approx -2.683281573$$

Ngā Upane mā te Kimi Pūtakerua

Me whakarea ngā taha e rua o te whārite ki te 6, arā, te tauraro pātahi he tino iti rawa te kitea o 2,3.

$$3\left(x+2\right)^{2}+2\left(x^{2}-18\right)=12x+12$$

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

$$3\left(x^{2}+4x+4\right)+2\left(x^{2}-18\right)=12x+12$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x^{2}+4x+4.

$$3x^{2}+12x+12+2\left(x^{2}-18\right)=12x+12$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te x^{2}-18.

$$3x^{2}+12x+12+2x^{2}-36=12x+12$$

Pahekotia te 3x^{2} me 2x^{2}, ka 5x^{2}.

$$5x^{2}+12x+12-36=12x+12$$

Tangohia te 36 i te 12, ka -24.

$$5x^{2}+12x-24=12x+12$$

Tangohia te 12x mai i ngā taha e rua.

$$5x^{2}+12x-24-12x=12$$

Pahekotia te 12x me -12x, ka 0.

$$5x^{2}-24=12$$

Me tāpiri te 24 ki ngā taha e rua.

$$5x^{2}=12+24$$

Tāpirihia te 12 ki te 24, ka 36.

$$5x^{2}=36$$

Whakawehea ngā taha e rua ki te 5.

$$x^{2}=\frac{36}{5}$$

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

$$x=\frac{6\sqrt{5}}{5} x=-\frac{6\sqrt{5}}{5}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me whakarea ngā taha e rua o te whārite ki te 6, arā, te tauraro pātahi he tino iti rawa te kitea o 2,3.

$$3\left(x+2\right)^{2}+2\left(x^{2}-18\right)=12x+12$$

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

$$3\left(x^{2}+4x+4\right)+2\left(x^{2}-18\right)=12x+12$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x^{2}+4x+4.

$$3x^{2}+12x+12+2\left(x^{2}-18\right)=12x+12$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te x^{2}-18.

$$3x^{2}+12x+12+2x^{2}-36=12x+12$$

Pahekotia te 3x^{2} me 2x^{2}, ka 5x^{2}.

$$5x^{2}+12x+12-36=12x+12$$

Tangohia te 36 i te 12, ka -24.

$$5x^{2}+12x-24=12x+12$$

Tangohia te 12x mai i ngā taha e rua.

$$5x^{2}+12x-24-12x=12$$

Pahekotia te 12x me -12x, ka 0.

$$5x^{2}-24=12$$

Tangohia te 12 mai i ngā taha e rua.

$$5x^{2}-24-12=0$$

Tangohia te 12 i te -24, ka -36.

$$5x^{2}-36=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, 0 mō b, me -36 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-36\right)}}{2\times 5}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-36\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{0±\sqrt{-20\left(-36\right)}}{2\times 5}$$

Whakareatia -20 ki te -36.

$$x=\frac{0±\sqrt{720}}{2\times 5}$$

Tuhia te pūtakerua o te 720.

$$x=\frac{0±12\sqrt{5}}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{0±12\sqrt{5}}{10}$$

Nā, me whakaoti te whārite x=\frac{0±12\sqrt{5}}{10} ina he tāpiri te ±.

$$x=\frac{6\sqrt{5}}{5}$$

Nā, me whakaoti te whārite x=\frac{0±12\sqrt{5}}{10} ina he tango te ±.

$$x=-\frac{6\sqrt{5}}{5}$$

Kua oti te whārite te whakatau.

$$x=\frac{6\sqrt{5}}{5} x=-\frac{6\sqrt{5}}{5}$$