Whakaoti i te x^2+10x+25=27

$$x ^ { 2 } + 10 x + 25 = 27$$

Whakaoti mō x

$$x=3\sqrt{3}-5\approx 0.196152423$$

$$x=-3\sqrt{3}-5\approx -10.196152423$$

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.

$$x^{2}+10x+25=27$$

Me tango 27 mai i ngā taha e rua o te whārite.

$$x^{2}+10x+25-27=27-27$$

Mā te tango i te 27 i a ia ake anō ka toe ko te 0.

$$x^{2}+10x+25-27=0$$

Tango 27 mai i 25.

$$x^{2}+10x-2=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 10 mō b, me -2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-10±\sqrt{10^{2}-4\left(-2\right)}}{2}$$

Pūrua 10.

$$x=\frac{-10±\sqrt{100-4\left(-2\right)}}{2}$$

Whakareatia -4 ki te -2.

$$x=\frac{-10±\sqrt{100+8}}{2}$$

Tāpiri 100 ki te 8.

$$x=\frac{-10±\sqrt{108}}{2}$$

Tuhia te pūtakerua o te 108.

$$x=\frac{-10±6\sqrt{3}}{2}$$

Nā, me whakaoti te whārite x=\frac{-10±6\sqrt{3}}{2} ina he tāpiri te ±. Tāpiri -10 ki te 6\sqrt{3}.

$$x=\frac{6\sqrt{3}-10}{2}$$

Whakawehe -10+6\sqrt{3} ki te 2.

$$x=3\sqrt{3}-5$$

Nā, me whakaoti te whārite x=\frac{-10±6\sqrt{3}}{2} ina he tango te ±. Tango 6\sqrt{3} mai i -10.

$$x=\frac{-6\sqrt{3}-10}{2}$$

Whakawehe -10-6\sqrt{3} ki te 2.

$$x=-3\sqrt{3}-5$$

Kua oti te whārite te whakatau.

$$x=3\sqrt{3}-5 x=-3\sqrt{3}-5$$

Ngā Upane mō te Whakaoti i te Pūrua

Tauwehea x^{2}+10x+25. 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}.

$$\left(x+5\right)^{2}=27$$

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

$$\sqrt{\left(x+5\right)^{2}}=\sqrt{27}$$

Whakarūnātia.

$$x+5=3\sqrt{3} x+5=-3\sqrt{3}$$

Me tango 5 mai i ngā taha e rua o te whārite.

$$x=3\sqrt{3}-5 x=-3\sqrt{3}-5$$