Whakaoti i te (100)^2+x^2=(2x+100)^2

$$( 100 ) ^ { 2 } + x ^ { 2 } = ( 2 x + 100 ) ^ { 2 }$$

Whakaoti mō x

$$x = -\frac{400}{3} = -133\frac{1}{3} \approx -133.333333333$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tātaihia te 100 mā te pū o 2, kia riro ko 10000.

$$10000+x^{2}=\left(2x+100\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(2x+100\right)^{2}.

$$10000+x^{2}=4x^{2}+400x+10000$$

Tangohia te 4x^{2} mai i ngā taha e rua.

$$10000+x^{2}-4x^{2}=400x+10000$$

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

$$10000-3x^{2}=400x+10000$$

Tangohia te 400x mai i ngā taha e rua.

$$10000-3x^{2}-400x=10000$$

Tangohia te 10000 mai i ngā taha e rua.

$$10000-3x^{2}-400x-10000=0$$

Tangohia te 10000 i te 10000, ka 0.

$$-3x^{2}-400x=0$$

Tauwehea te x.

$$x\left(-3x-400\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te -3x-400=0.

$$x=0 x=-\frac{400}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 100 mā te pū o 2, kia riro ko 10000.

$$10000+x^{2}=\left(2x+100\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(2x+100\right)^{2}.

$$10000+x^{2}=4x^{2}+400x+10000$$

Tangohia te 4x^{2} mai i ngā taha e rua.

$$10000+x^{2}-4x^{2}=400x+10000$$

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

$$10000-3x^{2}=400x+10000$$

Tangohia te 400x mai i ngā taha e rua.

$$10000-3x^{2}-400x=10000$$

Tangohia te 10000 mai i ngā taha e rua.

$$10000-3x^{2}-400x-10000=0$$

Tangohia te 10000 i te 10000, ka 0.

$$-3x^{2}-400x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -3 mō a, -400 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-400\right)±\sqrt{\left(-400\right)^{2}}}{2\left(-3\right)}$$

Tuhia te pūtakerua o te \left(-400\right)^{2}.

$$x=\frac{-\left(-400\right)±400}{2\left(-3\right)}$$

Ko te tauaro o -400 ko 400.

$$x=\frac{400±400}{2\left(-3\right)}$$

Whakareatia 2 ki te -3.

$$x=\frac{400±400}{-6}$$

Nā, me whakaoti te whārite x=\frac{400±400}{-6} ina he tāpiri te ±. Tāpiri 400 ki te 400.

$$x=\frac{800}{-6}$$

Whakahekea te hautanga \frac{800}{-6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=-\frac{400}{3}$$

Nā, me whakaoti te whārite x=\frac{400±400}{-6} ina he tango te ±. Tango 400 mai i 400.

$$x=\frac{0}{-6}$$

Whakawehe 0 ki te -6.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=-\frac{400}{3} x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Tātaihia te 100 mā te pū o 2, kia riro ko 10000.

$$10000+x^{2}=\left(2x+100\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(2x+100\right)^{2}.

$$10000+x^{2}=4x^{2}+400x+10000$$

Tangohia te 4x^{2} mai i ngā taha e rua.

$$10000+x^{2}-4x^{2}=400x+10000$$

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

$$10000-3x^{2}=400x+10000$$

Tangohia te 400x mai i ngā taha e rua.

$$10000-3x^{2}-400x=10000$$

Tangohia te 10000 mai i ngā taha e rua.

$$-3x^{2}-400x=10000-10000$$

Tangohia te 10000 i te 10000, ka 0.

$$-3x^{2}-400x=0$$

Whakawehea ngā taha e rua ki te -3.

$$\frac{-3x^{2}-400x}{-3}=\frac{0}{-3}$$

Mā te whakawehe ki te -3 ka wetekia te whakareanga ki te -3.

$$x^{2}+\left(-\frac{400}{-3}\right)x=\frac{0}{-3}$$

Whakawehe -400 ki te -3.

$$x^{2}+\frac{400}{3}x=\frac{0}{-3}$$

Whakawehe 0 ki te -3.

$$x^{2}+\frac{400}{3}x=0$$

Whakawehea te \frac{400}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{200}{3}. Nā, tāpiria te pūrua o te \frac{200}{3} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{400}{3}x+\left(\frac{200}{3}\right)^{2}=\left(\frac{200}{3}\right)^{2}$$

Pūruatia \frac{200}{3} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{400}{3}x+\frac{40000}{9}=\frac{40000}{9}$$

Tauwehea x^{2}+\frac{400}{3}x+\frac{40000}{9}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{200}{3}\right)^{2}=\frac{40000}{9}$$

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

$$\sqrt{\left(x+\frac{200}{3}\right)^{2}}=\sqrt{\frac{40000}{9}}$$

Whakarūnātia.

$$x+\frac{200}{3}=\frac{200}{3} x+\frac{200}{3}=-\frac{200}{3}$$

Me tango \frac{200}{3} mai i ngā taha e rua o te whārite.

$$x=0 x=-\frac{400}{3}$$