Whakaoti i te x^2+20x+17=-3

$${ x }^{ 2 } +20x+17=-3$$

Whakaoti mō x

$$x=4\sqrt{5}-10\approx -1.05572809$$

$$x=-4\sqrt{5}-10\approx -18.94427191$$

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.

$$x^{2}+20x+17=-3$$

Me tāpiri 3 ki ngā taha e rua o te whārite.

$$x^{2}+20x+17-\left(-3\right)=-3-\left(-3\right)$$

Mā te tango i te -3 i a ia ake anō ka toe ko te 0.

$$x^{2}+20x+17-\left(-3\right)=0$$

Tango -3 mai i 17.

$$x^{2}+20x+20=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 20 mō b, me 20 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-20±\sqrt{20^{2}-4\times 20}}{2}$$

Pūrua 20.

$$x=\frac{-20±\sqrt{400-4\times 20}}{2}$$

Whakareatia -4 ki te 20.

$$x=\frac{-20±\sqrt{400-80}}{2}$$

Tāpiri 400 ki te -80.

$$x=\frac{-20±\sqrt{320}}{2}$$

Tuhia te pūtakerua o te 320.

$$x=\frac{-20±8\sqrt{5}}{2}$$

Nā, me whakaoti te whārite x=\frac{-20±8\sqrt{5}}{2} ina he tāpiri te ±. Tāpiri -20 ki te 8\sqrt{5}.

$$x=\frac{8\sqrt{5}-20}{2}$$

Whakawehe -20+8\sqrt{5} ki te 2.

$$x=4\sqrt{5}-10$$

Nā, me whakaoti te whārite x=\frac{-20±8\sqrt{5}}{2} ina he tango te ±. Tango 8\sqrt{5} mai i -20.

$$x=\frac{-8\sqrt{5}-20}{2}$$

Whakawehe -20-8\sqrt{5} ki te 2.

$$x=-4\sqrt{5}-10$$

Kua oti te whārite te whakatau.

$$x=4\sqrt{5}-10 x=-4\sqrt{5}-10$$

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.

$$x^{2}+20x+17=-3$$

Me tango 17 mai i ngā taha e rua o te whārite.

$$x^{2}+20x+17-17=-3-17$$

Mā te tango i te 17 i a ia ake anō ka toe ko te 0.

$$x^{2}+20x=-3-17$$

Tango 17 mai i -3.

$$x^{2}+20x=-20$$

Whakawehea te 20, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 10. Nā, tāpiria te pūrua o te 10 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+20x+10^{2}=-20+10^{2}$$

Pūrua 10.

$$x^{2}+20x+100=-20+100$$

Tāpiri -20 ki te 100.

$$x^{2}+20x+100=80$$

Tauwehea x^{2}+20x+100. 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}.

$$\left(x+10\right)^{2}=80$$

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

$$\sqrt{\left(x+10\right)^{2}}=\sqrt{80}$$

Whakarūnātia.

$$x+10=4\sqrt{5} x+10=-4\sqrt{5}$$

Me tango 10 mai i ngā taha e rua o te whārite.

$$x=4\sqrt{5}-10 x=-4\sqrt{5}-10$$