Whakaoti i te x^2+5x-0.75=0

$$x ^ { 2 } + 5 x - 0.75 = 0$$

Whakaoti mō x

$$x=\sqrt{7}-2.5\approx 0.145751311$$

$$x=-\sqrt{7}-2.5\approx -5.145751311$$

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.

$$x^{2}+5x-0.75=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 5 mō b, me -0.75 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-5±\sqrt{5^{2}-4\left(-0.75\right)}}{2}$$

Pūrua 5.

$$x=\frac{-5±\sqrt{25-4\left(-0.75\right)}}{2}$$

Whakareatia -4 ki te -0.75.

$$x=\frac{-5±\sqrt{25+3}}{2}$$

Tāpiri 25 ki te 3.

$$x=\frac{-5±\sqrt{28}}{2}$$

Tuhia te pūtakerua o te 28.

$$x=\frac{-5±2\sqrt{7}}{2}$$

Nā, me whakaoti te whārite x=\frac{-5±2\sqrt{7}}{2} ina he tāpiri te ±. Tāpiri -5 ki te 2\sqrt{7}.

$$x=\frac{2\sqrt{7}-5}{2}$$

Whakawehe -5+2\sqrt{7} ki te 2.

$$x=\sqrt{7}-\frac{5}{2}$$

Nā, me whakaoti te whārite x=\frac{-5±2\sqrt{7}}{2} ina he tango te ±. Tango 2\sqrt{7} mai i -5.

$$x=\frac{-2\sqrt{7}-5}{2}$$

Whakawehe -5-2\sqrt{7} ki te 2.

$$x=-\sqrt{7}-\frac{5}{2}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{7}-\frac{5}{2} x=-\sqrt{7}-\frac{5}{2}$$

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.

$$x^{2}+5x-0.75=0$$

Me tāpiri 0.75 ki ngā taha e rua o te whārite.

$$x^{2}+5x-0.75-\left(-0.75\right)=-\left(-0.75\right)$$

Mā te tango i te -0.75 i a ia ake anō ka toe ko te 0.

$$x^{2}+5x=-\left(-0.75\right)$$

Tango -0.75 mai i 0.

$$x^{2}+5x=0.75$$

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

$$x^{2}+5x+\left(\frac{5}{2}\right)^{2}=0.75+\left(\frac{5}{2}\right)^{2}$$

Pūruatia \frac{5}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+5x+\frac{25}{4}=\frac{3+25}{4}$$

Tāpiri 0.75 ki te \frac{25}{4} 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.

$$x^{2}+5x+\frac{25}{4}=7$$

Tauwehea x^{2}+5x+\frac{25}{4}. 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}.

$$\left(x+\frac{5}{2}\right)^{2}=7$$

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

$$\sqrt{\left(x+\frac{5}{2}\right)^{2}}=\sqrt{7}$$

Whakarūnātia.

$$x+\frac{5}{2}=\sqrt{7} x+\frac{5}{2}=-\sqrt{7}$$

Me tango \frac{5}{2} mai i ngā taha e rua o te whārite.

$$x=\sqrt{7}-\frac{5}{2} x=-\sqrt{7}-\frac{5}{2}$$