Whakaoti i te x^2+7x=4x+20

$$x ^ { 2 } + 7 x = 4 x + 20$$

Whakaoti mō x

$$x = \frac{\sqrt{89} - 3}{2} \approx 3.216990566$$

$$x=\frac{-\sqrt{89}-3}{2}\approx -6.216990566$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 4x mai i ngā taha e rua.

$$x^{2}+7x-4x=20$$

Pahekotia te 7x me -4x, ka 3x.

$$x^{2}+3x=20$$

Tangohia te 20 mai i ngā taha e rua.

$$x^{2}+3x-20=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 3 mō b, me -20 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-3±\sqrt{3^{2}-4\left(-20\right)}}{2}$$

Pūrua 3.

$$x=\frac{-3±\sqrt{9-4\left(-20\right)}}{2}$$

Whakareatia -4 ki te -20.

$$x=\frac{-3±\sqrt{9+80}}{2}$$

Tāpiri 9 ki te 80.

$$x=\frac{-3±\sqrt{89}}{2}$$

Nā, me whakaoti te whārite x=\frac{-3±\sqrt{89}}{2} ina he tāpiri te ±. Tāpiri -3 ki te \sqrt{89}.

$$x=\frac{\sqrt{89}-3}{2}$$

Nā, me whakaoti te whārite x=\frac{-3±\sqrt{89}}{2} ina he tango te ±. Tango \sqrt{89} mai i -3.

$$x=\frac{-\sqrt{89}-3}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{89}-3}{2} x=\frac{-\sqrt{89}-3}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 4x mai i ngā taha e rua.

$$x^{2}+7x-4x=20$$

Pahekotia te 7x me -4x, ka 3x.

$$x^{2}+3x=20$$

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.

$$x^{2}+3x+\left(\frac{3}{2}\right)^{2}=20+\left(\frac{3}{2}\right)^{2}$$

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

$$x^{2}+3x+\frac{9}{4}=20+\frac{9}{4}$$

Tāpiri 20 ki te \frac{9}{4}.

$$x^{2}+3x+\frac{9}{4}=\frac{89}{4}$$

Tauwehea x^{2}+3x+\frac{9}{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}.

$$\left(x+\frac{3}{2}\right)^{2}=\frac{89}{4}$$

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

$$\sqrt{\left(x+\frac{3}{2}\right)^{2}}=\sqrt{\frac{89}{4}}$$

Whakarūnātia.

$$x+\frac{3}{2}=\frac{\sqrt{89}}{2} x+\frac{3}{2}=-\frac{\sqrt{89}}{2}$$

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

$$x=\frac{\sqrt{89}-3}{2} x=\frac{-\sqrt{89}-3}{2}$$