Whakaoti i te 4=-x^2+6x-5

$$4 = - x ^ { 2 } + 6 x - 5$$

Whakaoti mō x

$$x=3$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$-x^{2}+6x-5=4$$

Tangohia te 4 mai i ngā taha e rua.

$$-x^{2}+6x-5-4=0$$

Tangohia te 4 i te -5, ka -9.

$$-x^{2}+6x-9=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx-9. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=6 ab=-\left(-9\right)=9$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 9.

$$1,9 3,3$$

Tātaihia te tapeke mō ia takirua.

$$1+9=10 3+3=6$$

Ko te otinga te takirua ka hoatu i te tapeke 6.

$$a=3 b=3$$

Tuhia anō te -x^{2}+6x-9 hei \left(-x^{2}+3x\right)+\left(3x-9\right).

$$\left(-x^{2}+3x\right)+\left(3x-9\right)$$

Tauwehea te -x i te tuatahi me te 3 i te rōpū tuarua.

$$-x\left(x-3\right)+3\left(x-3\right)$$

Whakatauwehea atu te kīanga pātahi x-3 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-3\right)\left(-x+3\right)$$

Hei kimi otinga whārite, me whakaoti te x-3=0 me te -x+3=0.

$$x=3 x=3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$-x^{2}+6x-5=4$$

Tangohia te 4 mai i ngā taha e rua.

$$-x^{2}+6x-5-4=0$$

Tangohia te 4 i te -5, ka -9.

$$-x^{2}+6x-9=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 6 mō b, me -9 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-6±\sqrt{6^{2}-4\left(-1\right)\left(-9\right)}}{2\left(-1\right)}$$

Pūrua 6.

$$x=\frac{-6±\sqrt{36-4\left(-1\right)\left(-9\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-6±\sqrt{36+4\left(-9\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -9.

$$x=\frac{-6±\sqrt{36-36}}{2\left(-1\right)}$$

Tāpiri 36 ki te -36.

$$x=\frac{-6±\sqrt{0}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 0.

$$x=-\frac{6}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

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

Whakawehe -6 ki te -2.

$$x=3$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$-x^{2}+6x-5=4$$

Me tāpiri te 5 ki ngā taha e rua.

$$-x^{2}+6x=4+5$$

Tāpirihia te 4 ki te 5, ka 9.

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

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}+6x}{-1}=\frac{9}{-1}$$

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

$$x^{2}+\frac{6}{-1}x=\frac{9}{-1}$$

Whakawehe 6 ki te -1.

$$x^{2}-6x=\frac{9}{-1}$$

Whakawehe 9 ki te -1.

$$x^{2}-6x=-9$$

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.

$$x^{2}-6x+\left(-3\right)^{2}=-9+\left(-3\right)^{2}$$

Pūrua -3.

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

Tāpiri -9 ki te 9.

$$x^{2}-6x+9=0$$

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}.

$$\left(x-3\right)^{2}=0$$

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

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{0}$$

Whakarūnātia.

$$x-3=0 x-3=0$$

Me tāpiri 3 ki ngā taha e rua o te whārite.

$$x=3 x=3$$

Kua oti te whārite te whakatau. He ōrite ngā whakatau.

$$x=3$$