Whakaoti i te (2x+4)^2-(x-5)^2=26x

$$( 2 x + 4 ) ^ { 2 } - ( x - 5 ) ^ { 2 } = 26 x$$

Whakaoti mō x

$$x=\sqrt{3}\approx 1.732050808$$

$$x=-\sqrt{3}\approx -1.732050808$$

Ngā Upane mā te Kimi Pūtakerua

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(2x+4\right)^{2}.

$$4x^{2}+16x+16-\left(x-5\right)^{2}=26x$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-5\right)^{2}.

$$4x^{2}+16x+16-\left(x^{2}-10x+25\right)=26x$$

Hei kimi i te tauaro o x^{2}-10x+25, kimihia te tauaro o ia taurangi.

$$4x^{2}+16x+16-x^{2}+10x-25=26x$$

Pahekotia te 4x^{2} me -x^{2}, ka 3x^{2}.

$$3x^{2}+16x+16+10x-25=26x$$

Pahekotia te 16x me 10x, ka 26x.

$$3x^{2}+26x+16-25=26x$$

Tangohia te 25 i te 16, ka -9.

$$3x^{2}+26x-9=26x$$

Tangohia te 26x mai i ngā taha e rua.

$$3x^{2}+26x-9-26x=0$$

Pahekotia te 26x me -26x, ka 0.

$$3x^{2}-9=0$$

Me tāpiri te 9 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$3x^{2}=9$$

Whakawehea ngā taha e rua ki te 3.

$$x^{2}=\frac{9}{3}$$

Whakawehea te 9 ki te 3, kia riro ko 3.

$$x^{2}=3$$

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

$$x=\sqrt{3} x=-\sqrt{3}$$

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+4\right)^{2}.

$$4x^{2}+16x+16-\left(x-5\right)^{2}=26x$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-5\right)^{2}.

$$4x^{2}+16x+16-\left(x^{2}-10x+25\right)=26x$$

Hei kimi i te tauaro o x^{2}-10x+25, kimihia te tauaro o ia taurangi.

$$4x^{2}+16x+16-x^{2}+10x-25=26x$$

Pahekotia te 4x^{2} me -x^{2}, ka 3x^{2}.

$$3x^{2}+16x+16+10x-25=26x$$

Pahekotia te 16x me 10x, ka 26x.

$$3x^{2}+26x+16-25=26x$$

Tangohia te 25 i te 16, ka -9.

$$3x^{2}+26x-9=26x$$

Tangohia te 26x mai i ngā taha e rua.

$$3x^{2}+26x-9-26x=0$$

Pahekotia te 26x me -26x, ka 0.

$$3x^{2}-9=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, 0 mō b, me -9 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-9\right)}}{2\times 3}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-9\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{0±\sqrt{-12\left(-9\right)}}{2\times 3}$$

Whakareatia -12 ki te -9.

$$x=\frac{0±\sqrt{108}}{2\times 3}$$

Tuhia te pūtakerua o te 108.

$$x=\frac{0±6\sqrt{3}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{0±6\sqrt{3}}{6}$$

Nā, me whakaoti te whārite x=\frac{0±6\sqrt{3}}{6} ina he tāpiri te ±.

$$x=\sqrt{3}$$

Nā, me whakaoti te whārite x=\frac{0±6\sqrt{3}}{6} ina he tango te ±.

$$x=-\sqrt{3}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{3} x=-\sqrt{3}$$