Whakaoti i te x^2+100x+2500=0

$$x ^ { 2 } + 100 x + 2500 = 0$$

Whakaoti mō x

$$x=-50$$

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.

$$x^{2}+100x+2500=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 100 mō b, me 2500 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-100±\sqrt{100^{2}-4\times 2500}}{2}$$

Pūrua 100.

$$x=\frac{-100±\sqrt{10000-4\times 2500}}{2}$$

Whakareatia -4 ki te 2500.

$$x=\frac{-100±\sqrt{10000-10000}}{2}$$

Tāpiri 10000 ki te -10000.

$$x=\frac{-100±\sqrt{0}}{2}$$

Tuhia te pūtakerua o te 0.

$$x=-\frac{100}{2}$$

Whakawehe -100 ki te 2.

$$x=-50$$

Ngā Upane mō te Whakaoti i te Pūrua

Tauwehea x^{2}+100x+2500. 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}.

$$\left(x+50\right)^{2}=0$$

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

$$\sqrt{\left(x+50\right)^{2}}=\sqrt{0}$$

Whakarūnātia.

$$x+50=0 x+50=0$$

Me tango 50 mai i ngā taha e rua o te whārite.

$$x=-50 x=-50$$

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

$$x=-50$$