Whakaoti i te x^2+3x+5/4=0

$$x ^ { 2 } + 3 x + \frac { 5 } { 4 } = 0$$

Whakaoti mō x

$$x = -\frac{5}{2} = -2\frac{1}{2} = -2.5$$

$$x=-\frac{1}{2}=-0.5$$

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.

$$x^{2}+3x+\frac{5}{4}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 3 mō b, me \frac{5}{4} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-3±\sqrt{3^{2}-4\times \frac{5}{4}}}{2}$$

Pūrua 3.

$$x=\frac{-3±\sqrt{9-4\times \frac{5}{4}}}{2}$$

Whakareatia -4 ki te \frac{5}{4}.

$$x=\frac{-3±\sqrt{9-5}}{2}$$

Tāpiri 9 ki te -5.

$$x=\frac{-3±\sqrt{4}}{2}$$

Tuhia te pūtakerua o te 4.

$$x=\frac{-3±2}{2}$$

Nā, me whakaoti te whārite x=\frac{-3±2}{2} ina he tāpiri te ±. Tāpiri -3 ki te 2.

$$x=-\frac{1}{2}$$

Nā, me whakaoti te whārite x=\frac{-3±2}{2} ina he tango te ±. Tango 2 mai i -3.

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

Kua oti te whārite te whakatau.

$$x=-\frac{1}{2} x=-\frac{5}{2}$$

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.

$$x^{2}+3x+\frac{5}{4}=0$$

Me tango \frac{5}{4} mai i ngā taha e rua o te whārite.

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

Mā te tango i te \frac{5}{4} i a ia ake anō ka toe ko te 0.

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

Whakawehea te 3, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{3}{2}. Nā, tāpiria te pūrua o te \frac{3}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+3x+\left(\frac{3}{2}\right)^{2}=-\frac{5}{4}+\left(\frac{3}{2}\right)^{2}$$

Pūruatia \frac{3}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+3x+\frac{9}{4}=\frac{-5+9}{4}$$

Tāpiri -\frac{5}{4} ki te \frac{9}{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.

$$x^{2}+3x+\frac{9}{4}=1$$

Tauwehea te x^{2}+3x+\frac{9}{4}. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{3}{2}\right)^{2}=1$$

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

$$\sqrt{\left(x+\frac{3}{2}\right)^{2}}=\sqrt{1}$$

Whakarūnātia.

$$x+\frac{3}{2}=1 x+\frac{3}{2}=-1$$

Me tango \frac{3}{2} mai i ngā taha e rua o te whārite.

$$x=-\frac{1}{2} x=-\frac{5}{2}$$