Whakaoti i te 4(x+1)(x-2)=-(1+2x)^2

$$4 ( x + 1 ) ( x - 2 ) = - ( 1 + 2 x ) ^ { 2 }$$

Whakaoti mō x

$$x=\frac{\sqrt{14}}{4}\approx 0.935414347$$

$$x=-\frac{\sqrt{14}}{4}\approx -0.935414347$$

Ngā Upane mā te Kimi Pūtakerua

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x+1.

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

Whakamahia te āhuatanga tuaritanga hei whakarea te 4x+4 ki te x-2 ka whakakotahi i ngā kupu rite.

$$4x^{2}-4x-8=-\left(1+2x\right)^{2}$$

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

$$4x^{2}-4x-8=-\left(1+4x+4x^{2}\right)$$

Hei kimi i te tauaro o 1+4x+4x^{2}, kimihia te tauaro o ia taurangi.

$$4x^{2}-4x-8=-1-4x-4x^{2}$$

Me tāpiri te 4x ki ngā taha e rua.

$$4x^{2}-4x-8+4x=-1-4x^{2}$$

Pahekotia te -4x me 4x, ka 0.

$$4x^{2}-8=-1-4x^{2}$$

Me tāpiri te 4x^{2} ki ngā taha e rua.

$$4x^{2}-8+4x^{2}=-1$$

Pahekotia te 4x^{2} me 4x^{2}, ka 8x^{2}.

$$8x^{2}-8=-1$$

Me tāpiri te 8 ki ngā taha e rua.

$$8x^{2}=-1+8$$

Tāpirihia te -1 ki te 8, ka 7.

$$8x^{2}=7$$

Whakawehea ngā taha e rua ki te 8.

$$x^{2}=\frac{7}{8}$$

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

$$x=\frac{\sqrt{14}}{4} x=-\frac{\sqrt{14}}{4}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x+1.

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

Whakamahia te āhuatanga tuaritanga hei whakarea te 4x+4 ki te x-2 ka whakakotahi i ngā kupu rite.

$$4x^{2}-4x-8=-\left(1+2x\right)^{2}$$

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

$$4x^{2}-4x-8=-\left(1+4x+4x^{2}\right)$$

Hei kimi i te tauaro o 1+4x+4x^{2}, kimihia te tauaro o ia taurangi.

$$4x^{2}-4x-8=-1-4x-4x^{2}$$

Tangohia te -1 mai i ngā taha e rua.

$$4x^{2}-4x-8-\left(-1\right)=-4x-4x^{2}$$

Ko te tauaro o -1 ko 1.

$$4x^{2}-4x-8+1=-4x-4x^{2}$$

Me tāpiri te 4x ki ngā taha e rua.

$$4x^{2}-4x-8+1+4x=-4x^{2}$$

Tāpirihia te -8 ki te 1, ka -7.

$$4x^{2}-4x-7+4x=-4x^{2}$$

Pahekotia te -4x me 4x, ka 0.

$$4x^{2}-7=-4x^{2}$$

Me tāpiri te 4x^{2} ki ngā taha e rua.

$$4x^{2}-7+4x^{2}=0$$

Pahekotia te 4x^{2} me 4x^{2}, ka 8x^{2}.

$$8x^{2}-7=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 8 mō a, 0 mō b, me -7 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\left(-7\right)}}{2\times 8}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 8\left(-7\right)}}{2\times 8}$$

Whakareatia -4 ki te 8.

$$x=\frac{0±\sqrt{-32\left(-7\right)}}{2\times 8}$$

Whakareatia -32 ki te -7.

$$x=\frac{0±\sqrt{224}}{2\times 8}$$

Tuhia te pūtakerua o te 224.

$$x=\frac{0±4\sqrt{14}}{2\times 8}$$

Whakareatia 2 ki te 8.

$$x=\frac{0±4\sqrt{14}}{16}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{14}}{16} ina he tāpiri te ±.

$$x=\frac{\sqrt{14}}{4}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{14}}{16} ina he tango te ±.

$$x=-\frac{\sqrt{14}}{4}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{14}}{4} x=-\frac{\sqrt{14}}{4}$$