Whakaoti i te 4.9x^2+2x-15=0

$$4.9 { x }^{ 2 } +2x-15=0$$

Whakaoti mō x

$$x = \frac{5 \sqrt{298} - 10}{49} \approx 1.55741597$$

$$x=\frac{-5\sqrt{298}-10}{49}\approx -1.965579235$$

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.

$$4.9x^{2}+2x-15=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4.9 mō a, 2 mō b, me -15 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2±\sqrt{2^{2}-4\times 4.9\left(-15\right)}}{2\times 4.9}$$

Pūrua 2.

$$x=\frac{-2±\sqrt{4-4\times 4.9\left(-15\right)}}{2\times 4.9}$$

Whakareatia -4 ki te 4.9.

$$x=\frac{-2±\sqrt{4-19.6\left(-15\right)}}{2\times 4.9}$$

Whakareatia -19.6 ki te -15.

$$x=\frac{-2±\sqrt{4+294}}{2\times 4.9}$$

Tāpiri 4 ki te 294.

$$x=\frac{-2±\sqrt{298}}{2\times 4.9}$$

Whakareatia 2 ki te 4.9.

$$x=\frac{-2±\sqrt{298}}{9.8}$$

Nā, me whakaoti te whārite x=\frac{-2±\sqrt{298}}{9.8} ina he tāpiri te ±. Tāpiri -2 ki te \sqrt{298}.

$$x=\frac{\sqrt{298}-2}{9.8}$$

Whakawehe -2+\sqrt{298} ki te 9.8 mā te whakarea -2+\sqrt{298} ki te tau huripoki o 9.8.

$$x=\frac{5\sqrt{298}-10}{49}$$

Nā, me whakaoti te whārite x=\frac{-2±\sqrt{298}}{9.8} ina he tango te ±. Tango \sqrt{298} mai i -2.

$$x=\frac{-\sqrt{298}-2}{9.8}$$

Whakawehe -2-\sqrt{298} ki te 9.8 mā te whakarea -2-\sqrt{298} ki te tau huripoki o 9.8.

$$x=\frac{-5\sqrt{298}-10}{49}$$

Kua oti te whārite te whakatau.

$$x=\frac{5\sqrt{298}-10}{49} x=\frac{-5\sqrt{298}-10}{49}$$

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.

$$4.9x^{2}+2x-15=0$$

Me tāpiri 15 ki ngā taha e rua o te whārite.

$$4.9x^{2}+2x-15-\left(-15\right)=-\left(-15\right)$$

Mā te tango i te -15 i a ia ake anō ka toe ko te 0.

$$4.9x^{2}+2x=-\left(-15\right)$$

Tango -15 mai i 0.

$$4.9x^{2}+2x=15$$

Whakawehea ngā taha e rua o te whārite ki te 4.9, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{4.9x^{2}+2x}{4.9}=\frac{15}{4.9}$$

Mā te whakawehe ki te 4.9 ka wetekia te whakareanga ki te 4.9.

$$x^{2}+\frac{2}{4.9}x=\frac{15}{4.9}$$

Whakawehe 2 ki te 4.9 mā te whakarea 2 ki te tau huripoki o 4.9.

$$x^{2}+\frac{20}{49}x=\frac{15}{4.9}$$

Whakawehe 15 ki te 4.9 mā te whakarea 15 ki te tau huripoki o 4.9.

$$x^{2}+\frac{20}{49}x=\frac{150}{49}$$

Whakawehea te \frac{20}{49}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{10}{49}. Nā, tāpiria te pūrua o te \frac{10}{49} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{20}{49}x+\frac{10}{49}^{2}=\frac{150}{49}+\frac{10}{49}^{2}$$

Pūruatia \frac{10}{49} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{20}{49}x+\frac{100}{2401}=\frac{150}{49}+\frac{100}{2401}$$

Tāpiri \frac{150}{49} ki te \frac{100}{2401} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}+\frac{20}{49}x+\frac{100}{2401}=\frac{7450}{2401}$$

Tauwehea x^{2}+\frac{20}{49}x+\frac{100}{2401}. 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}.

$$\left(x+\frac{10}{49}\right)^{2}=\frac{7450}{2401}$$

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

$$\sqrt{\left(x+\frac{10}{49}\right)^{2}}=\sqrt{\frac{7450}{2401}}$$

Whakarūnātia.

$$x+\frac{10}{49}=\frac{5\sqrt{298}}{49} x+\frac{10}{49}=-\frac{5\sqrt{298}}{49}$$

Me tango \frac{10}{49} mai i ngā taha e rua o te whārite.

$$x=\frac{5\sqrt{298}-10}{49} x=\frac{-5\sqrt{298}-10}{49}$$