Whakaoti i te 60x^2+588x-169=0

$$60 x ^ { 2 } + 588 x - 169 = 0$$

Whakaoti mō x

$$x=\frac{2\sqrt{1509}}{15}-\frac{49}{10}\approx 0.27944656$$

$$x=-\frac{2\sqrt{1509}}{15}-\frac{49}{10}\approx -10.07944656$$

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.

$$60x^{2}+588x-169=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 60 mō a, 588 mō b, me -169 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-588±\sqrt{588^{2}-4\times 60\left(-169\right)}}{2\times 60}$$

Pūrua 588.

$$x=\frac{-588±\sqrt{345744-4\times 60\left(-169\right)}}{2\times 60}$$

Whakareatia -4 ki te 60.

$$x=\frac{-588±\sqrt{345744-240\left(-169\right)}}{2\times 60}$$

Whakareatia -240 ki te -169.

$$x=\frac{-588±\sqrt{345744+40560}}{2\times 60}$$

Tāpiri 345744 ki te 40560.

$$x=\frac{-588±\sqrt{386304}}{2\times 60}$$

Tuhia te pūtakerua o te 386304.

$$x=\frac{-588±16\sqrt{1509}}{2\times 60}$$

Whakareatia 2 ki te 60.

$$x=\frac{-588±16\sqrt{1509}}{120}$$

Nā, me whakaoti te whārite x=\frac{-588±16\sqrt{1509}}{120} ina he tāpiri te ±. Tāpiri -588 ki te 16\sqrt{1509}.

$$x=\frac{16\sqrt{1509}-588}{120}$$

Whakawehe -588+16\sqrt{1509} ki te 120.

$$x=\frac{2\sqrt{1509}}{15}-\frac{49}{10}$$

Nā, me whakaoti te whārite x=\frac{-588±16\sqrt{1509}}{120} ina he tango te ±. Tango 16\sqrt{1509} mai i -588.

$$x=\frac{-16\sqrt{1509}-588}{120}$$

Whakawehe -588-16\sqrt{1509} ki te 120.

$$x=-\frac{2\sqrt{1509}}{15}-\frac{49}{10}$$

Kua oti te whārite te whakatau.

$$x=\frac{2\sqrt{1509}}{15}-\frac{49}{10} x=-\frac{2\sqrt{1509}}{15}-\frac{49}{10}$$

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.

$$60x^{2}+588x-169=0$$

Me tāpiri 169 ki ngā taha e rua o te whārite.

$$60x^{2}+588x-169-\left(-169\right)=-\left(-169\right)$$

Mā te tango i te -169 i a ia ake anō ka toe ko te 0.

$$60x^{2}+588x=-\left(-169\right)$$

Tango -169 mai i 0.

$$60x^{2}+588x=169$$

Whakawehea ngā taha e rua ki te 60.

$$\frac{60x^{2}+588x}{60}=\frac{169}{60}$$

Mā te whakawehe ki te 60 ka wetekia te whakareanga ki te 60.

$$x^{2}+\frac{588}{60}x=\frac{169}{60}$$

Whakahekea te hautanga \frac{588}{60} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 12.

$$x^{2}+\frac{49}{5}x=\frac{169}{60}$$

Whakawehea te \frac{49}{5}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{49}{10}. Nā, tāpiria te pūrua o te \frac{49}{10} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{49}{5}x+\left(\frac{49}{10}\right)^{2}=\frac{169}{60}+\left(\frac{49}{10}\right)^{2}$$

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

$$x^{2}+\frac{49}{5}x+\frac{2401}{100}=\frac{169}{60}+\frac{2401}{100}$$

Tāpiri \frac{169}{60} ki te \frac{2401}{100} 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.

$$x^{2}+\frac{49}{5}x+\frac{2401}{100}=\frac{2012}{75}$$

Tauwehea x^{2}+\frac{49}{5}x+\frac{2401}{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}.

$$\left(x+\frac{49}{10}\right)^{2}=\frac{2012}{75}$$

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

$$\sqrt{\left(x+\frac{49}{10}\right)^{2}}=\sqrt{\frac{2012}{75}}$$

Whakarūnātia.

$$x+\frac{49}{10}=\frac{2\sqrt{1509}}{15} x+\frac{49}{10}=-\frac{2\sqrt{1509}}{15}$$

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

$$x=\frac{2\sqrt{1509}}{15}-\frac{49}{10} x=-\frac{2\sqrt{1509}}{15}-\frac{49}{10}$$