Whakaoti i te x^2+4x=9(3/4)

$$x ^ { 2 } + 4 x = 9 ( 3 / 4 )$$

Whakaoti mō x

$$x=\frac{\sqrt{43}}{2}-2\approx 1.278719262$$

$$x=-\frac{\sqrt{43}}{2}-2\approx -5.278719262$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 9 ki te \frac{3}{4}, ka \frac{27}{4}.

$$x^{2}+4x=\frac{27}{4}$$

Tangohia te \frac{27}{4} mai i ngā taha e rua.

$$x^{2}+4x-\frac{27}{4}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 4 mō b, me -\frac{27}{4} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-4±\sqrt{4^{2}-4\left(-\frac{27}{4}\right)}}{2}$$

Pūrua 4.

$$x=\frac{-4±\sqrt{16-4\left(-\frac{27}{4}\right)}}{2}$$

Whakareatia -4 ki te -\frac{27}{4}.

$$x=\frac{-4±\sqrt{16+27}}{2}$$

Tāpiri 16 ki te 27.

$$x=\frac{-4±\sqrt{43}}{2}$$

Nā, me whakaoti te whārite x=\frac{-4±\sqrt{43}}{2} ina he tāpiri te ±. Tāpiri -4 ki te \sqrt{43}.

$$x=\frac{\sqrt{43}-4}{2}$$

Whakawehe -4+\sqrt{43} ki te 2.

$$x=\frac{\sqrt{43}}{2}-2$$

Nā, me whakaoti te whārite x=\frac{-4±\sqrt{43}}{2} ina he tango te ±. Tango \sqrt{43} mai i -4.

$$x=\frac{-\sqrt{43}-4}{2}$$

Whakawehe -4-\sqrt{43} ki te 2.

$$x=-\frac{\sqrt{43}}{2}-2$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{43}}{2}-2 x=-\frac{\sqrt{43}}{2}-2$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te 9 ki te \frac{3}{4}, ka \frac{27}{4}.

$$x^{2}+4x=\frac{27}{4}$$

Whakawehea te 4, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 2. Nā, tāpiria te pūrua o te 2 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+4x+2^{2}=\frac{27}{4}+2^{2}$$

Pūrua 2.

$$x^{2}+4x+4=\frac{27}{4}+4$$

Tāpiri \frac{27}{4} ki te 4.

$$x^{2}+4x+4=\frac{43}{4}$$

Tauwehea te x^{2}+4x+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}.

$$\left(x+2\right)^{2}=\frac{43}{4}$$

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

$$\sqrt{\left(x+2\right)^{2}}=\sqrt{\frac{43}{4}}$$

Whakarūnātia.

$$x+2=\frac{\sqrt{43}}{2} x+2=-\frac{\sqrt{43}}{2}$$

Me tango 2 mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{43}}{2}-2 x=-\frac{\sqrt{43}}{2}-2$$