Whakaoti i te 76+x*(1126-x)=x*x

$$76+x \times (1126-x)=x \times x$$

Whakaoti mō x

$$x = \frac{\sqrt{317121} + 563}{2} \approx 563.06748747$$

$$x=\frac{563-\sqrt{317121}}{2}\approx -0.06748747$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te x ki te x, ka x^{2}.

$$76+x\left(1126-x\right)=x^{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 1126-x.

$$76+1126x-x^{2}=x^{2}$$

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

$$76+1126x-x^{2}-x^{2}=0$$

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

$$76+1126x-2x^{2}=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$-2x^{2}+1126x+76=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -2 mō a, 1126 mō b, me 76 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1126±\sqrt{1126^{2}-4\left(-2\right)\times 76}}{2\left(-2\right)}$$

Pūrua 1126.

$$x=\frac{-1126±\sqrt{1267876-4\left(-2\right)\times 76}}{2\left(-2\right)}$$

Whakareatia -4 ki te -2.

$$x=\frac{-1126±\sqrt{1267876+8\times 76}}{2\left(-2\right)}$$

Whakareatia 8 ki te 76.

$$x=\frac{-1126±\sqrt{1267876+608}}{2\left(-2\right)}$$

Tāpiri 1267876 ki te 608.

$$x=\frac{-1126±\sqrt{1268484}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te 1268484.

$$x=\frac{-1126±2\sqrt{317121}}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=\frac{-1126±2\sqrt{317121}}{-4}$$

Nā, me whakaoti te whārite x=\frac{-1126±2\sqrt{317121}}{-4} ina he tāpiri te ±. Tāpiri -1126 ki te 2\sqrt{317121}.

$$x=\frac{2\sqrt{317121}-1126}{-4}$$

Whakawehe -1126+2\sqrt{317121} ki te -4.

$$x=\frac{563-\sqrt{317121}}{2}$$

Nā, me whakaoti te whārite x=\frac{-1126±2\sqrt{317121}}{-4} ina he tango te ±. Tango 2\sqrt{317121} mai i -1126.

$$x=\frac{-2\sqrt{317121}-1126}{-4}$$

Whakawehe -1126-2\sqrt{317121} ki te -4.

$$x=\frac{\sqrt{317121}+563}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{563-\sqrt{317121}}{2} x=\frac{\sqrt{317121}+563}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te x ki te x, ka x^{2}.

$$76+x\left(1126-x\right)=x^{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 1126-x.

$$76+1126x-x^{2}=x^{2}$$

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

$$76+1126x-x^{2}-x^{2}=0$$

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

$$76+1126x-2x^{2}=0$$

Tangohia te 76 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$1126x-2x^{2}=-76$$

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$-2x^{2}+1126x=-76$$

Whakawehea ngā taha e rua ki te -2.

$$\frac{-2x^{2}+1126x}{-2}=-\frac{76}{-2}$$

Mā te whakawehe ki te -2 ka wetekia te whakareanga ki te -2.

$$x^{2}+\frac{1126}{-2}x=-\frac{76}{-2}$$

Whakawehe 1126 ki te -2.

$$x^{2}-563x=-\frac{76}{-2}$$

Whakawehe -76 ki te -2.

$$x^{2}-563x=38$$

Whakawehea te -563, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{563}{2}. Nā, tāpiria te pūrua o te -\frac{563}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-563x+\left(-\frac{563}{2}\right)^{2}=38+\left(-\frac{563}{2}\right)^{2}$$

Pūruatia -\frac{563}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-563x+\frac{316969}{4}=38+\frac{316969}{4}$$

Tāpiri 38 ki te \frac{316969}{4}.

$$x^{2}-563x+\frac{316969}{4}=\frac{317121}{4}$$

Tauwehea x^{2}-563x+\frac{316969}{4}. 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}.

$$\left(x-\frac{563}{2}\right)^{2}=\frac{317121}{4}$$

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

$$\sqrt{\left(x-\frac{563}{2}\right)^{2}}=\sqrt{\frac{317121}{4}}$$

Whakarūnātia.

$$x-\frac{563}{2}=\frac{\sqrt{317121}}{2} x-\frac{563}{2}=-\frac{\sqrt{317121}}{2}$$

Me tāpiri \frac{563}{2} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{317121}+563}{2} x=\frac{563-\sqrt{317121}}{2}$$