Whakaoti i te x^2+1*80x-5*40=0

$$x ^ { 2 } + 1 \cdot 80 x - 5 \cdot 40 = 0$$

Whakaoti mō x

$$x=30\sqrt{2}-40\approx 2.426406871$$

$$x=-30\sqrt{2}-40\approx -82.426406871$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 1 ki te 80, ka 80.

$$x^{2}+80x-5\times 40=0$$

Whakareatia te 5 ki te 40, ka 200.

$$x^{2}+80x-200=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 80 mō b, me -200 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-80±\sqrt{80^{2}-4\left(-200\right)}}{2}$$

Pūrua 80.

$$x=\frac{-80±\sqrt{6400-4\left(-200\right)}}{2}$$

Whakareatia -4 ki te -200.

$$x=\frac{-80±\sqrt{6400+800}}{2}$$

Tāpiri 6400 ki te 800.

$$x=\frac{-80±\sqrt{7200}}{2}$$

Tuhia te pūtakerua o te 7200.

$$x=\frac{-80±60\sqrt{2}}{2}$$

Nā, me whakaoti te whārite x=\frac{-80±60\sqrt{2}}{2} ina he tāpiri te ±. Tāpiri -80 ki te 60\sqrt{2}.

$$x=\frac{60\sqrt{2}-80}{2}$$

Whakawehe -80+60\sqrt{2} ki te 2.

$$x=30\sqrt{2}-40$$

Nā, me whakaoti te whārite x=\frac{-80±60\sqrt{2}}{2} ina he tango te ±. Tango 60\sqrt{2} mai i -80.

$$x=\frac{-60\sqrt{2}-80}{2}$$

Whakawehe -80-60\sqrt{2} ki te 2.

$$x=-30\sqrt{2}-40$$

Kua oti te whārite te whakatau.

$$x=30\sqrt{2}-40 x=-30\sqrt{2}-40$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te 1 ki te 80, ka 80.

$$x^{2}+80x-5\times 40=0$$

Whakareatia te 5 ki te 40, ka 200.

$$x^{2}+80x-200=0$$

Me tāpiri te 200 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$x^{2}+80x=200$$

Whakawehea te 80, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 40. Nā, tāpiria te pūrua o te 40 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+80x+40^{2}=200+40^{2}$$

Pūrua 40.

$$x^{2}+80x+1600=200+1600$$

Tāpiri 200 ki te 1600.

$$x^{2}+80x+1600=1800$$

Tauwehea x^{2}+80x+1600. 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}.

$$\left(x+40\right)^{2}=1800$$

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

$$\sqrt{\left(x+40\right)^{2}}=\sqrt{1800}$$

Whakarūnātia.

$$x+40=30\sqrt{2} x+40=-30\sqrt{2}$$

Me tango 40 mai i ngā taha e rua o te whārite.

$$x=30\sqrt{2}-40 x=-30\sqrt{2}-40$$