Whakaoti i te (x-4)(x-4)-(4x+5)(3x-10)=17x-110quad5?

$$( x - 4 ) ( x - 4 ) - ( 4 x + 5 ) ( 3 x - 10 ) = 17 x - 110 \quad 5 ?$$

Whakaoti mō x

$$x=2\sqrt{14}\approx 7.483314774$$

$$x=-2\sqrt{14}\approx -7.483314774$$

Ngā Upane mā te Kimi Pūtakerua

Whakareatia te x-4 ki te x-4, ka \left(x-4\right)^{2}.

$$\left(x-4\right)^{2}-\left(4x+5\right)\left(3x-10\right)=17x-110\times 5$$

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

$$x^{2}-8x+16-\left(4x+5\right)\left(3x-10\right)=17x-110\times 5$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 4x+5 ki te 3x-10 ka whakakotahi i ngā kupu rite.

$$x^{2}-8x+16-\left(12x^{2}-25x-50\right)=17x-110\times 5$$

Hei kimi i te tauaro o 12x^{2}-25x-50, kimihia te tauaro o ia taurangi.

$$x^{2}-8x+16-12x^{2}+25x+50=17x-110\times 5$$

Pahekotia te x^{2} me -12x^{2}, ka -11x^{2}.

$$-11x^{2}-8x+16+25x+50=17x-110\times 5$$

Pahekotia te -8x me 25x, ka 17x.

$$-11x^{2}+17x+16+50=17x-110\times 5$$

Tāpirihia te 16 ki te 50, ka 66.

$$-11x^{2}+17x+66=17x-110\times 5$$

Whakareatia te 110 ki te 5, ka 550.

$$-11x^{2}+17x+66=17x-550$$

Tangohia te 17x mai i ngā taha e rua.

$$-11x^{2}+17x+66-17x=-550$$

Pahekotia te 17x me -17x, ka 0.

$$-11x^{2}+66=-550$$

Tangohia te 66 mai i ngā taha e rua.

$$-11x^{2}=-550-66$$

Tangohia te 66 i te -550, ka -616.

$$-11x^{2}=-616$$

Whakawehea ngā taha e rua ki te -11.

$$x^{2}=\frac{-616}{-11}$$

Whakawehea te -616 ki te -11, kia riro ko 56.

$$x^{2}=56$$

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

$$x=2\sqrt{14} x=-2\sqrt{14}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te x-4 ki te x-4, ka \left(x-4\right)^{2}.

$$\left(x-4\right)^{2}-\left(4x+5\right)\left(3x-10\right)=17x-110\times 5$$

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

$$x^{2}-8x+16-\left(4x+5\right)\left(3x-10\right)=17x-110\times 5$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 4x+5 ki te 3x-10 ka whakakotahi i ngā kupu rite.

$$x^{2}-8x+16-\left(12x^{2}-25x-50\right)=17x-110\times 5$$

Hei kimi i te tauaro o 12x^{2}-25x-50, kimihia te tauaro o ia taurangi.

$$x^{2}-8x+16-12x^{2}+25x+50=17x-110\times 5$$

Pahekotia te x^{2} me -12x^{2}, ka -11x^{2}.

$$-11x^{2}-8x+16+25x+50=17x-110\times 5$$

Pahekotia te -8x me 25x, ka 17x.

$$-11x^{2}+17x+16+50=17x-110\times 5$$

Tāpirihia te 16 ki te 50, ka 66.

$$-11x^{2}+17x+66=17x-110\times 5$$

Whakareatia te 110 ki te 5, ka 550.

$$-11x^{2}+17x+66=17x-550$$

Tangohia te 17x mai i ngā taha e rua.

$$-11x^{2}+17x+66-17x=-550$$

Pahekotia te 17x me -17x, ka 0.

$$-11x^{2}+66=-550$$

Me tāpiri te 550 ki ngā taha e rua.

$$-11x^{2}+66+550=0$$

Tāpirihia te 66 ki te 550, ka 616.

$$-11x^{2}+616=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -11 mō a, 0 mō b, me 616 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-11\right)\times 616}}{2\left(-11\right)}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-11\right)\times 616}}{2\left(-11\right)}$$

Whakareatia -4 ki te -11.

$$x=\frac{0±\sqrt{44\times 616}}{2\left(-11\right)}$$

Whakareatia 44 ki te 616.

$$x=\frac{0±\sqrt{27104}}{2\left(-11\right)}$$

Tuhia te pūtakerua o te 27104.

$$x=\frac{0±44\sqrt{14}}{2\left(-11\right)}$$

Whakareatia 2 ki te -11.

$$x=\frac{0±44\sqrt{14}}{-22}$$

Nā, me whakaoti te whārite x=\frac{0±44\sqrt{14}}{-22} ina he tāpiri te ±.

$$x=-2\sqrt{14}$$

Nā, me whakaoti te whārite x=\frac{0±44\sqrt{14}}{-22} ina he tango te ±.

$$x=2\sqrt{14}$$

Kua oti te whārite te whakatau.

$$x=-2\sqrt{14} x=2\sqrt{14}$$