Whakaoti i te x^2+76x-76*1126=0

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

Whakaoti mō x

$$x=2\sqrt{21755}-38\approx 256.991525302$$

$$x=-2\sqrt{21755}-38\approx -332.991525302$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 76 ki te 1126, ka 85576.

$$x^{2}+76x-85576=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 76 mō b, me -85576 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-76±\sqrt{76^{2}-4\left(-85576\right)}}{2}$$

Pūrua 76.

$$x=\frac{-76±\sqrt{5776-4\left(-85576\right)}}{2}$$

Whakareatia -4 ki te -85576.

$$x=\frac{-76±\sqrt{5776+342304}}{2}$$

Tāpiri 5776 ki te 342304.

$$x=\frac{-76±\sqrt{348080}}{2}$$

Tuhia te pūtakerua o te 348080.

$$x=\frac{-76±4\sqrt{21755}}{2}$$

Nā, me whakaoti te whārite x=\frac{-76±4\sqrt{21755}}{2} ina he tāpiri te ±. Tāpiri -76 ki te 4\sqrt{21755}.

$$x=\frac{4\sqrt{21755}-76}{2}$$

Whakawehe -76+4\sqrt{21755} ki te 2.

$$x=2\sqrt{21755}-38$$

Nā, me whakaoti te whārite x=\frac{-76±4\sqrt{21755}}{2} ina he tango te ±. Tango 4\sqrt{21755} mai i -76.

$$x=\frac{-4\sqrt{21755}-76}{2}$$

Whakawehe -76-4\sqrt{21755} ki te 2.

$$x=-2\sqrt{21755}-38$$

Kua oti te whārite te whakatau.

$$x=2\sqrt{21755}-38 x=-2\sqrt{21755}-38$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te 76 ki te 1126, ka 85576.

$$x^{2}+76x-85576=0$$

Me tāpiri te 85576 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$x^{2}+76x=85576$$

Whakawehea te 76, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 38. Nā, tāpiria te pūrua o te 38 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+76x+38^{2}=85576+38^{2}$$

Pūrua 38.

$$x^{2}+76x+1444=85576+1444$$

Tāpiri 85576 ki te 1444.

$$x^{2}+76x+1444=87020$$

Tauwehea x^{2}+76x+1444. 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}.

$$\left(x+38\right)^{2}=87020$$

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

$$\sqrt{\left(x+38\right)^{2}}=\sqrt{87020}$$

Whakarūnātia.

$$x+38=2\sqrt{21755} x+38=-2\sqrt{21755}$$

Me tango 38 mai i ngā taha e rua o te whārite.

$$x=2\sqrt{21755}-38 x=-2\sqrt{21755}-38$$