Whakaoti i te -2s^2+52s=90

$$- 2 s ^ { 2 } + 52 s = 90$$

Whakaoti mō s

$$s=2\sqrt{31}+13\approx 24.135528726$$

$$s=13-2\sqrt{31}\approx 1.864471274$$

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.

$$-2s^{2}+52s=90$$

Me tango 90 mai i ngā taha e rua o te whārite.

$$-2s^{2}+52s-90=90-90$$

Mā te tango i te 90 i a ia ake anō ka toe ko te 0.

$$-2s^{2}+52s-90=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -2 mō a, 52 mō b, me -90 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$s=\frac{-52±\sqrt{52^{2}-4\left(-2\right)\left(-90\right)}}{2\left(-2\right)}$$

Pūrua 52.

$$s=\frac{-52±\sqrt{2704-4\left(-2\right)\left(-90\right)}}{2\left(-2\right)}$$

Whakareatia -4 ki te -2.

$$s=\frac{-52±\sqrt{2704+8\left(-90\right)}}{2\left(-2\right)}$$

Whakareatia 8 ki te -90.

$$s=\frac{-52±\sqrt{2704-720}}{2\left(-2\right)}$$

Tāpiri 2704 ki te -720.

$$s=\frac{-52±\sqrt{1984}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te 1984.

$$s=\frac{-52±8\sqrt{31}}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$s=\frac{-52±8\sqrt{31}}{-4}$$

Nā, me whakaoti te whārite s=\frac{-52±8\sqrt{31}}{-4} ina he tāpiri te ±. Tāpiri -52 ki te 8\sqrt{31}.

$$s=\frac{8\sqrt{31}-52}{-4}$$

Whakawehe -52+8\sqrt{31} ki te -4.

$$s=13-2\sqrt{31}$$

Nā, me whakaoti te whārite s=\frac{-52±8\sqrt{31}}{-4} ina he tango te ±. Tango 8\sqrt{31} mai i -52.

$$s=\frac{-8\sqrt{31}-52}{-4}$$

Whakawehe -52-8\sqrt{31} ki te -4.

$$s=2\sqrt{31}+13$$

Kua oti te whārite te whakatau.

$$s=13-2\sqrt{31} s=2\sqrt{31}+13$$

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.

$$-2s^{2}+52s=90$$

Whakawehea ngā taha e rua ki te -2.

$$\frac{-2s^{2}+52s}{-2}=\frac{90}{-2}$$

Mā te whakawehe ki te -2 ka wetekia te whakareanga ki te -2.

$$s^{2}+\frac{52}{-2}s=\frac{90}{-2}$$

Whakawehe 52 ki te -2.

$$s^{2}-26s=\frac{90}{-2}$$

Whakawehe 90 ki te -2.

$$s^{2}-26s=-45$$

Whakawehea te -26, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -13. Nā, tāpiria te pūrua o te -13 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$s^{2}-26s+\left(-13\right)^{2}=-45+\left(-13\right)^{2}$$

Pūrua -13.

$$s^{2}-26s+169=-45+169$$

Tāpiri -45 ki te 169.

$$s^{2}-26s+169=124$$

Tauwehea s^{2}-26s+169. 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}.

$$\left(s-13\right)^{2}=124$$

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

$$\sqrt{\left(s-13\right)^{2}}=\sqrt{124}$$

Whakarūnātia.

$$s-13=2\sqrt{31} s-13=-2\sqrt{31}$$

Me tāpiri 13 ki ngā taha e rua o te whārite.

$$s=2\sqrt{31}+13 s=13-2\sqrt{31}$$