Whakaoti i te 6x^2+12x+14=7x^2-5

$$6 x ^ { 2 } + 12 x + 14 = 7 x ^ { 2 } - 5$$

Whakaoti mō x

$$x=\sqrt{55}+6\approx 13.416198487$$

$$x=6-\sqrt{55}\approx -1.416198487$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 7x^{2} mai i ngā taha e rua.

$$6x^{2}+12x+14-7x^{2}=-5$$

Pahekotia te 6x^{2} me -7x^{2}, ka -x^{2}.

$$-x^{2}+12x+14=-5$$

Me tāpiri te 5 ki ngā taha e rua.

$$-x^{2}+12x+14+5=0$$

Tāpirihia te 14 ki te 5, ka 19.

$$-x^{2}+12x+19=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 12 mō b, me 19 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-12±\sqrt{12^{2}-4\left(-1\right)\times 19}}{2\left(-1\right)}$$

Pūrua 12.

$$x=\frac{-12±\sqrt{144-4\left(-1\right)\times 19}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-12±\sqrt{144+4\times 19}}{2\left(-1\right)}$$

Whakareatia 4 ki te 19.

$$x=\frac{-12±\sqrt{144+76}}{2\left(-1\right)}$$

Tāpiri 144 ki te 76.

$$x=\frac{-12±\sqrt{220}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 220.

$$x=\frac{-12±2\sqrt{55}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-12±2\sqrt{55}}{-2}$$

Nā, me whakaoti te whārite x=\frac{-12±2\sqrt{55}}{-2} ina he tāpiri te ±. Tāpiri -12 ki te 2\sqrt{55}.

$$x=\frac{2\sqrt{55}-12}{-2}$$

Whakawehe -12+2\sqrt{55} ki te -2.

$$x=6-\sqrt{55}$$

Nā, me whakaoti te whārite x=\frac{-12±2\sqrt{55}}{-2} ina he tango te ±. Tango 2\sqrt{55} mai i -12.

$$x=\frac{-2\sqrt{55}-12}{-2}$$

Whakawehe -12-2\sqrt{55} ki te -2.

$$x=\sqrt{55}+6$$

Kua oti te whārite te whakatau.

$$x=6-\sqrt{55} x=\sqrt{55}+6$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 7x^{2} mai i ngā taha e rua.

$$6x^{2}+12x+14-7x^{2}=-5$$

Pahekotia te 6x^{2} me -7x^{2}, ka -x^{2}.

$$-x^{2}+12x+14=-5$$

Tangohia te 14 mai i ngā taha e rua.

$$-x^{2}+12x=-5-14$$

Tangohia te 14 i te -5, ka -19.

$$-x^{2}+12x=-19$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}+12x}{-1}=-\frac{19}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$x^{2}+\frac{12}{-1}x=-\frac{19}{-1}$$

Whakawehe 12 ki te -1.

$$x^{2}-12x=-\frac{19}{-1}$$

Whakawehe -19 ki te -1.

$$x^{2}-12x=19$$

Whakawehea te -12, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -6. Nā, tāpiria te pūrua o te -6 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-12x+\left(-6\right)^{2}=19+\left(-6\right)^{2}$$

Pūrua -6.

$$x^{2}-12x+36=19+36$$

Tāpiri 19 ki te 36.

$$x^{2}-12x+36=55$$

Tauwehea x^{2}-12x+36. 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}.

$$\left(x-6\right)^{2}=55$$

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

$$\sqrt{\left(x-6\right)^{2}}=\sqrt{55}$$

Whakarūnātia.

$$x-6=\sqrt{55} x-6=-\sqrt{55}$$

Me tāpiri 6 ki ngā taha e rua o te whārite.

$$x=\sqrt{55}+6 x=6-\sqrt{55}$$