Whakaoti i te (2x+1)^2+(x+1)^2=6x+47

$$( 2 x + 1 ) ^ { 2 } + ( x + 1 ) ^ { 2 } = 6 x + 47$$

Whakaoti mō x

$$x=-3$$

$$x=3$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(2x+1\right)^{2}.

$$4x^{2}+4x+1+\left(x+1\right)^{2}=6x+47$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+1\right)^{2}.

$$4x^{2}+4x+1+x^{2}+2x+1=6x+47$$

Pahekotia te 4x^{2} me x^{2}, ka 5x^{2}.

$$5x^{2}+4x+1+2x+1=6x+47$$

Pahekotia te 4x me 2x, ka 6x.

$$5x^{2}+6x+1+1=6x+47$$

Tāpirihia te 1 ki te 1, ka 2.

$$5x^{2}+6x+2=6x+47$$

Tangohia te 6x mai i ngā taha e rua.

$$5x^{2}+6x+2-6x=47$$

Pahekotia te 6x me -6x, ka 0.

$$5x^{2}+2=47$$

Tangohia te 47 mai i ngā taha e rua.

$$5x^{2}+2-47=0$$

Tangohia te 47 i te 2, ka -45.

$$5x^{2}-45=0$$

Whakawehea ngā taha e rua ki te 5.

$$x^{2}-9=0$$

Whakaarohia te x^{2}-9. Tuhia anō te x^{2}-9 hei x^{2}-3^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

Hei kimi otinga whārite, me whakaoti te x-3=0 me te x+3=0.

$$x=3 x=-3$$

Ngā Upane mā te Kimi Pūtakerua

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(2x+1\right)^{2}.

$$4x^{2}+4x+1+\left(x+1\right)^{2}=6x+47$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+1\right)^{2}.

$$4x^{2}+4x+1+x^{2}+2x+1=6x+47$$

Pahekotia te 4x^{2} me x^{2}, ka 5x^{2}.

$$5x^{2}+4x+1+2x+1=6x+47$$

Pahekotia te 4x me 2x, ka 6x.

$$5x^{2}+6x+1+1=6x+47$$

Tāpirihia te 1 ki te 1, ka 2.

$$5x^{2}+6x+2=6x+47$$

Tangohia te 6x mai i ngā taha e rua.

$$5x^{2}+6x+2-6x=47$$

Pahekotia te 6x me -6x, ka 0.

$$5x^{2}+2=47$$

Tangohia te 2 mai i ngā taha e rua.

$$5x^{2}=47-2$$

Tangohia te 2 i te 47, ka 45.

$$5x^{2}=45$$

Whakawehea ngā taha e rua ki te 5.

$$x^{2}=\frac{45}{5}$$

Whakawehea te 45 ki te 5, kia riro ko 9.

$$x^{2}=9$$

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

$$x=3 x=-3$$

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(2x+1\right)^{2}.

$$4x^{2}+4x+1+\left(x+1\right)^{2}=6x+47$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+1\right)^{2}.

$$4x^{2}+4x+1+x^{2}+2x+1=6x+47$$

Pahekotia te 4x^{2} me x^{2}, ka 5x^{2}.

$$5x^{2}+4x+1+2x+1=6x+47$$

Pahekotia te 4x me 2x, ka 6x.

$$5x^{2}+6x+1+1=6x+47$$

Tāpirihia te 1 ki te 1, ka 2.

$$5x^{2}+6x+2=6x+47$$

Tangohia te 6x mai i ngā taha e rua.

$$5x^{2}+6x+2-6x=47$$

Pahekotia te 6x me -6x, ka 0.

$$5x^{2}+2=47$$

Tangohia te 47 mai i ngā taha e rua.

$$5x^{2}+2-47=0$$

Tangohia te 47 i te 2, ka -45.

$$5x^{2}-45=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, 0 mō b, me -45 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-45\right)}}{2\times 5}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-45\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{0±\sqrt{-20\left(-45\right)}}{2\times 5}$$

Whakareatia -20 ki te -45.

$$x=\frac{0±\sqrt{900}}{2\times 5}$$

Tuhia te pūtakerua o te 900.

$$x=\frac{0±30}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{0±30}{10}$$

Nā, me whakaoti te whārite x=\frac{0±30}{10} ina he tāpiri te ±. Whakawehe 30 ki te 10.

$$x=3$$

Nā, me whakaoti te whārite x=\frac{0±30}{10} ina he tango te ±. Whakawehe -30 ki te 10.

$$x=-3$$

Kua oti te whārite te whakatau.

$$x=3 x=-3$$