Whakaoti i te 3x^2+10x-1=2x^2+4x+153

$$3 x ^ { 2 } + 10 x - 1 = 2 x ^ { 2 } + 4 x + 153$$

Whakaoti mō x

$$x=\sqrt{163}-3\approx 9.767145335$$

$$x=-\left(\sqrt{163}+3\right)\approx -15.767145335$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 2x^{2} mai i ngā taha e rua.

$$3x^{2}+10x-1-2x^{2}=4x+153$$

Pahekotia te 3x^{2} me -2x^{2}, ka x^{2}.

$$x^{2}+10x-1=4x+153$$

Tangohia te 4x mai i ngā taha e rua.

$$x^{2}+10x-1-4x=153$$

Pahekotia te 10x me -4x, ka 6x.

$$x^{2}+6x-1=153$$

Tangohia te 153 mai i ngā taha e rua.

$$x^{2}+6x-1-153=0$$

Tangohia te 153 i te -1, ka -154.

$$x^{2}+6x-154=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 6 mō b, me -154 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-6±\sqrt{6^{2}-4\left(-154\right)}}{2}$$

Pūrua 6.

$$x=\frac{-6±\sqrt{36-4\left(-154\right)}}{2}$$

Whakareatia -4 ki te -154.

$$x=\frac{-6±\sqrt{36+616}}{2}$$

Tāpiri 36 ki te 616.

$$x=\frac{-6±\sqrt{652}}{2}$$

Tuhia te pūtakerua o te 652.

$$x=\frac{-6±2\sqrt{163}}{2}$$

Nā, me whakaoti te whārite x=\frac{-6±2\sqrt{163}}{2} ina he tāpiri te ±. Tāpiri -6 ki te 2\sqrt{163}.

$$x=\frac{2\sqrt{163}-6}{2}$$

Whakawehe -6+2\sqrt{163} ki te 2.

$$x=\sqrt{163}-3$$

Nā, me whakaoti te whārite x=\frac{-6±2\sqrt{163}}{2} ina he tango te ±. Tango 2\sqrt{163} mai i -6.

$$x=\frac{-2\sqrt{163}-6}{2}$$

Whakawehe -6-2\sqrt{163} ki te 2.

$$x=-\sqrt{163}-3$$

Kua oti te whārite te whakatau.

$$x=\sqrt{163}-3 x=-\sqrt{163}-3$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 2x^{2} mai i ngā taha e rua.

$$3x^{2}+10x-1-2x^{2}=4x+153$$

Pahekotia te 3x^{2} me -2x^{2}, ka x^{2}.

$$x^{2}+10x-1=4x+153$$

Tangohia te 4x mai i ngā taha e rua.

$$x^{2}+10x-1-4x=153$$

Pahekotia te 10x me -4x, ka 6x.

$$x^{2}+6x-1=153$$

Me tāpiri te 1 ki ngā taha e rua.

$$x^{2}+6x=153+1$$

Tāpirihia te 153 ki te 1, ka 154.

$$x^{2}+6x=154$$

Whakawehea te 6, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 3. Nā, tāpiria te pūrua o te 3 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+6x+3^{2}=154+3^{2}$$

Pūrua 3.

$$x^{2}+6x+9=154+9$$

Tāpiri 154 ki te 9.

$$x^{2}+6x+9=163$$

Tauwehea x^{2}+6x+9. 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}.

$$\left(x+3\right)^{2}=163$$

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

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{163}$$

Whakarūnātia.

$$x+3=\sqrt{163} x+3=-\sqrt{163}$$

Me tango 3 mai i ngā taha e rua o te whārite.

$$x=\sqrt{163}-3 x=-\sqrt{163}-3$$