Whakaoti i te x^2=12x+17

$$x ^ { 2 } = 12 x + 17$$

Whakaoti mō x

$$x=\sqrt{53}+6\approx 13.280109889$$

$$x=6-\sqrt{53}\approx -1.280109889$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 12x mai i ngā taha e rua.

$$x^{2}-12x=17$$

Tangohia te 17 mai i ngā taha e rua.

$$x^{2}-12x-17=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -12 mō b, me -17 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\left(-17\right)}}{2}$$

Pūrua -12.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\left(-17\right)}}{2}$$

Whakareatia -4 ki te -17.

$$x=\frac{-\left(-12\right)±\sqrt{144+68}}{2}$$

Tāpiri 144 ki te 68.

$$x=\frac{-\left(-12\right)±\sqrt{212}}{2}$$

Tuhia te pūtakerua o te 212.

$$x=\frac{-\left(-12\right)±2\sqrt{53}}{2}$$

Ko te tauaro o -12 ko 12.

$$x=\frac{12±2\sqrt{53}}{2}$$

Nā, me whakaoti te whārite x=\frac{12±2\sqrt{53}}{2} ina he tāpiri te ±. Tāpiri 12 ki te 2\sqrt{53}.

$$x=\frac{2\sqrt{53}+12}{2}$$

Whakawehe 12+2\sqrt{53} ki te 2.

$$x=\sqrt{53}+6$$

Nā, me whakaoti te whārite x=\frac{12±2\sqrt{53}}{2} ina he tango te ±. Tango 2\sqrt{53} mai i 12.

$$x=\frac{12-2\sqrt{53}}{2}$$

Whakawehe 12-2\sqrt{53} ki te 2.

$$x=6-\sqrt{53}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{53}+6 x=6-\sqrt{53}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 12x mai i ngā taha e rua.

$$x^{2}-12x=17$$

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.

$$x^{2}-12x+\left(-6\right)^{2}=17+\left(-6\right)^{2}$$

Pūrua -6.

$$x^{2}-12x+36=17+36$$

Tāpiri 17 ki te 36.

$$x^{2}-12x+36=53$$

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}.

$$\left(x-6\right)^{2}=53$$

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

$$\sqrt{\left(x-6\right)^{2}}=\sqrt{53}$$

Whakarūnātia.

$$x-6=\sqrt{53} x-6=-\sqrt{53}$$

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

$$x=\sqrt{53}+6 x=6-\sqrt{53}$$