Whakaoti i te x^2+2x+4=22x+9

$${ x }^{ 2 } +2x+4=22x+9$$

Whakaoti mō x

$$x=\sqrt{105}+10\approx 20.246950766$$

$$x=10-\sqrt{105}\approx -0.246950766$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 22x mai i ngā taha e rua.

$$x^{2}+2x+4-22x=9$$

Pahekotia te 2x me -22x, ka -20x.

$$x^{2}-20x+4=9$$

Tangohia te 9 mai i ngā taha e rua.

$$x^{2}-20x+4-9=0$$

Tangohia te 9 i te 4, ka -5.

$$x^{2}-20x-5=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -20 mō b, me -5 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}-4\left(-5\right)}}{2}$$

Pūrua -20.

$$x=\frac{-\left(-20\right)±\sqrt{400-4\left(-5\right)}}{2}$$

Whakareatia -4 ki te -5.

$$x=\frac{-\left(-20\right)±\sqrt{400+20}}{2}$$

Tāpiri 400 ki te 20.

$$x=\frac{-\left(-20\right)±\sqrt{420}}{2}$$

Tuhia te pūtakerua o te 420.

$$x=\frac{-\left(-20\right)±2\sqrt{105}}{2}$$

Ko te tauaro o -20 ko 20.

$$x=\frac{20±2\sqrt{105}}{2}$$

Nā, me whakaoti te whārite x=\frac{20±2\sqrt{105}}{2} ina he tāpiri te ±. Tāpiri 20 ki te 2\sqrt{105}.

$$x=\frac{2\sqrt{105}+20}{2}$$

Whakawehe 20+2\sqrt{105} ki te 2.

$$x=\sqrt{105}+10$$

Nā, me whakaoti te whārite x=\frac{20±2\sqrt{105}}{2} ina he tango te ±. Tango 2\sqrt{105} mai i 20.

$$x=\frac{20-2\sqrt{105}}{2}$$

Whakawehe 20-2\sqrt{105} ki te 2.

$$x=10-\sqrt{105}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{105}+10 x=10-\sqrt{105}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 22x mai i ngā taha e rua.

$$x^{2}+2x+4-22x=9$$

Pahekotia te 2x me -22x, ka -20x.

$$x^{2}-20x+4=9$$

Tangohia te 4 mai i ngā taha e rua.

$$x^{2}-20x=9-4$$

Tangohia te 4 i te 9, ka 5.

$$x^{2}-20x=5$$

Whakawehea te -20, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -10. Nā, tāpiria te pūrua o te -10 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-20x+\left(-10\right)^{2}=5+\left(-10\right)^{2}$$

Pūrua -10.

$$x^{2}-20x+100=5+100$$

Tāpiri 5 ki te 100.

$$x^{2}-20x+100=105$$

Tauwehea x^{2}-20x+100. 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}.

$$\left(x-10\right)^{2}=105$$

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

$$\sqrt{\left(x-10\right)^{2}}=\sqrt{105}$$

Whakarūnātia.

$$x-10=\sqrt{105} x-10=-\sqrt{105}$$

Me tāpiri 10 ki ngā taha e rua o te whārite.

$$x=\sqrt{105}+10 x=10-\sqrt{105}$$