Whakaoti i te -5x^2+1800x-130000=32000

$$-5 { x }^{ 2 } +1800x-130000=32000$$

Whakaoti mō x

$$x=180$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$-5x^{2}+1800x-130000=32000$$

Me tango 32000 mai i ngā taha e rua o te whārite.

$$-5x^{2}+1800x-130000-32000=32000-32000$$

Mā te tango i te 32000 i a ia ake anō ka toe ko te 0.

$$-5x^{2}+1800x-130000-32000=0$$

Tango 32000 mai i -130000.

$$-5x^{2}+1800x-162000=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -5 mō a, 1800 mō b, me -162000 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1800±\sqrt{1800^{2}-4\left(-5\right)\left(-162000\right)}}{2\left(-5\right)}$$

Pūrua 1800.

$$x=\frac{-1800±\sqrt{3240000-4\left(-5\right)\left(-162000\right)}}{2\left(-5\right)}$$

Whakareatia -4 ki te -5.

$$x=\frac{-1800±\sqrt{3240000+20\left(-162000\right)}}{2\left(-5\right)}$$

Whakareatia 20 ki te -162000.

$$x=\frac{-1800±\sqrt{3240000-3240000}}{2\left(-5\right)}$$

Tāpiri 3240000 ki te -3240000.

$$x=\frac{-1800±\sqrt{0}}{2\left(-5\right)}$$

Tuhia te pūtakerua o te 0.

$$x=-\frac{1800}{2\left(-5\right)}$$

Whakareatia 2 ki te -5.

$$x=-\frac{1800}{-10}$$

Whakawehe -1800 ki te -10.

$$x=180$$

Ngā Upane mō te Whakaoti i te Pūrua

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.

$$-5x^{2}+1800x-130000=32000$$

Me tāpiri 130000 ki ngā taha e rua o te whārite.

$$-5x^{2}+1800x-130000-\left(-130000\right)=32000-\left(-130000\right)$$

Mā te tango i te -130000 i a ia ake anō ka toe ko te 0.

$$-5x^{2}+1800x=32000-\left(-130000\right)$$

Tango -130000 mai i 32000.

$$-5x^{2}+1800x=162000$$

Whakawehea ngā taha e rua ki te -5.

$$\frac{-5x^{2}+1800x}{-5}=\frac{162000}{-5}$$

Mā te whakawehe ki te -5 ka wetekia te whakareanga ki te -5.

$$x^{2}+\frac{1800}{-5}x=\frac{162000}{-5}$$

Whakawehe 1800 ki te -5.

$$x^{2}-360x=\frac{162000}{-5}$$

Whakawehe 162000 ki te -5.

$$x^{2}-360x=-32400$$

Whakawehea te -360, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -180. Nā, tāpiria te pūrua o te -180 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-360x+\left(-180\right)^{2}=-32400+\left(-180\right)^{2}$$

Pūrua -180.

$$x^{2}-360x+32400=-32400+32400$$

Tāpiri -32400 ki te 32400.

$$x^{2}-360x+32400=0$$

Tauwehea x^{2}-360x+32400. 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}.

$$\left(x-180\right)^{2}=0$$

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

$$\sqrt{\left(x-180\right)^{2}}=\sqrt{0}$$

Whakarūnātia.

$$x-180=0 x-180=0$$

Me tāpiri 180 ki ngā taha e rua o te whārite.

$$x=180 x=180$$

Kua oti te whārite te whakatau. He ōrite ngā whakatau.

$$x=180$$