Whakaoti i te 3x^2+3.5x+1=63

$$3 { x }^{ 2 } +3.5x+1=63$$

Whakaoti mō x

$$x = -\frac{31}{6} = -5\frac{1}{6} \approx -5.166666667$$

$$x=4$$

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.

$$3x^{2}+3.5x+1=63$$

Me tango 63 mai i ngā taha e rua o te whārite.

$$3x^{2}+3.5x+1-63=63-63$$

Mā te tango i te 63 i a ia ake anō ka toe ko te 0.

$$3x^{2}+3.5x+1-63=0$$

Tango 63 mai i 1.

$$3x^{2}+3.5x-62=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, 3.5 mō b, me -62 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-3.5±\sqrt{3.5^{2}-4\times 3\left(-62\right)}}{2\times 3}$$

Pūruatia 3.5 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-3.5±\sqrt{12.25-4\times 3\left(-62\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-3.5±\sqrt{12.25-12\left(-62\right)}}{2\times 3}$$

Whakareatia -12 ki te -62.

$$x=\frac{-3.5±\sqrt{12.25+744}}{2\times 3}$$

Tāpiri 12.25 ki te 744.

$$x=\frac{-3.5±\sqrt{756.25}}{2\times 3}$$

Tuhia te pūtakerua o te 756.25.

$$x=\frac{-3.5±\frac{55}{2}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{-3.5±\frac{55}{2}}{6}$$

Nā, me whakaoti te whārite x=\frac{-3.5±\frac{55}{2}}{6} ina he tāpiri te ±. Tāpiri -3.5 ki te \frac{55}{2} 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.

$$x=\frac{24}{6}$$

Whakawehe 24 ki te 6.

$$x=4$$

Nā, me whakaoti te whārite x=\frac{-3.5±\frac{55}{2}}{6} ina he tango te ±. Tango \frac{55}{2} mai i -3.5 mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x=-\frac{31}{6}$$

Kua oti te whārite te whakatau.

$$x=4 x=-\frac{31}{6}$$

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.

$$3x^{2}+3.5x+1=63$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$3x^{2}+3.5x+1-1=63-1$$

Mā te tango i te 1 i a ia ake anō ka toe ko te 0.

$$3x^{2}+3.5x=63-1$$

Tango 1 mai i 63.

$$3x^{2}+3.5x=62$$

Whakawehea ngā taha e rua ki te 3.

$$\frac{3x^{2}+3.5x}{3}=\frac{62}{3}$$

Mā te whakawehe ki te 3 ka wetekia te whakareanga ki te 3.

$$x^{2}+\frac{3.5}{3}x=\frac{62}{3}$$

Whakawehe 3.5 ki te 3.

$$x^{2}+\frac{7}{6}x=\frac{62}{3}$$

Whakawehea te \frac{7}{6}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{7}{12}. Nā, tāpiria te pūrua o te \frac{7}{12} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{7}{6}x+\frac{7}{12}^{2}=\frac{62}{3}+\frac{7}{12}^{2}$$

Pūruatia \frac{7}{12} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{7}{6}x+\frac{49}{144}=\frac{62}{3}+\frac{49}{144}$$

Tāpiri \frac{62}{3} ki te \frac{49}{144} 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.

$$x^{2}+\frac{7}{6}x+\frac{49}{144}=\frac{3025}{144}$$

Tauwehea x^{2}+\frac{7}{6}x+\frac{49}{144}. 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}.

$$\left(x+\frac{7}{12}\right)^{2}=\frac{3025}{144}$$

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

$$\sqrt{\left(x+\frac{7}{12}\right)^{2}}=\sqrt{\frac{3025}{144}}$$

Whakarūnātia.

$$x+\frac{7}{12}=\frac{55}{12} x+\frac{7}{12}=-\frac{55}{12}$$

Me tango \frac{7}{12} mai i ngā taha e rua o te whārite.

$$x=4 x=-\frac{31}{6}$$