Whakaoti i te -793x+9left(x-15right)+4left(x-4right)x/x=0

$$-793x+9 \left( x-15 \right) +4 \left( x-4 \right) \frac{ x }{ x } =0$$

Whakaoti mō x

$$x=-\frac{151}{780}\approx -0.193589744$$

Ngā Upane Whakamahi Tauwehe

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$-793xx+9\left(x-15\right)x+4\left(x-4\right)x=0$$

Whakareatia te x ki te x, ka x^{2}.

$$-793x^{2}+9\left(x-15\right)x+4\left(x-4\right)x=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 9 ki te x-15.

$$-793x^{2}+\left(9x-135\right)x+4\left(x-4\right)x=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 9x-135 ki te x.

$$-793x^{2}+9x^{2}-135x+4\left(x-4\right)x=0$$

Pahekotia te -793x^{2} me 9x^{2}, ka -784x^{2}.

$$-784x^{2}-135x+4\left(x-4\right)x=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x-4.

$$-784x^{2}-135x+\left(4x-16\right)x=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4x-16 ki te x.

$$-784x^{2}-135x+4x^{2}-16x=0$$

Pahekotia te -784x^{2} me 4x^{2}, ka -780x^{2}.

$$-780x^{2}-135x-16x=0$$

Pahekotia te -135x me -16x, ka -151x.

$$-780x^{2}-151x=0$$

Tauwehea te x.

$$x\left(-780x-151\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te -780x-151=0.

$$x=0 x=-\frac{151}{780}$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=-\frac{151}{780}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$-793xx+9\left(x-15\right)x+4\left(x-4\right)x=0$$

Whakareatia te x ki te x, ka x^{2}.

$$-793x^{2}+9\left(x-15\right)x+4\left(x-4\right)x=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 9 ki te x-15.

$$-793x^{2}+\left(9x-135\right)x+4\left(x-4\right)x=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 9x-135 ki te x.

$$-793x^{2}+9x^{2}-135x+4\left(x-4\right)x=0$$

Pahekotia te -793x^{2} me 9x^{2}, ka -784x^{2}.

$$-784x^{2}-135x+4\left(x-4\right)x=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x-4.

$$-784x^{2}-135x+\left(4x-16\right)x=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4x-16 ki te x.

$$-784x^{2}-135x+4x^{2}-16x=0$$

Pahekotia te -784x^{2} me 4x^{2}, ka -780x^{2}.

$$-780x^{2}-135x-16x=0$$

Pahekotia te -135x me -16x, ka -151x.

$$-780x^{2}-151x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -780 mō a, -151 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-151\right)±\sqrt{\left(-151\right)^{2}}}{2\left(-780\right)}$$

Tuhia te pūtakerua o te \left(-151\right)^{2}.

$$x=\frac{-\left(-151\right)±151}{2\left(-780\right)}$$

Ko te tauaro o -151 ko 151.

$$x=\frac{151±151}{2\left(-780\right)}$$

Whakareatia 2 ki te -780.

$$x=\frac{151±151}{-1560}$$

Nā, me whakaoti te whārite x=\frac{151±151}{-1560} ina he tāpiri te ±. Tāpiri 151 ki te 151.

$$x=\frac{302}{-1560}$$

Whakahekea te hautanga \frac{302}{-1560} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=-\frac{151}{780}$$

Nā, me whakaoti te whārite x=\frac{151±151}{-1560} ina he tango te ±. Tango 151 mai i 151.

$$x=\frac{0}{-1560}$$

Whakawehe 0 ki te -1560.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=-\frac{151}{780} x=0$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=-\frac{151}{780}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$-793xx+9\left(x-15\right)x+4\left(x-4\right)x=0$$

Whakareatia te x ki te x, ka x^{2}.

$$-793x^{2}+9\left(x-15\right)x+4\left(x-4\right)x=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 9 ki te x-15.

$$-793x^{2}+\left(9x-135\right)x+4\left(x-4\right)x=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 9x-135 ki te x.

$$-793x^{2}+9x^{2}-135x+4\left(x-4\right)x=0$$

Pahekotia te -793x^{2} me 9x^{2}, ka -784x^{2}.

$$-784x^{2}-135x+4\left(x-4\right)x=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x-4.

$$-784x^{2}-135x+\left(4x-16\right)x=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4x-16 ki te x.

$$-784x^{2}-135x+4x^{2}-16x=0$$

Pahekotia te -784x^{2} me 4x^{2}, ka -780x^{2}.

$$-780x^{2}-135x-16x=0$$

Pahekotia te -135x me -16x, ka -151x.

$$-780x^{2}-151x=0$$

Whakawehea ngā taha e rua ki te -780.

$$\frac{-780x^{2}-151x}{-780}=\frac{0}{-780}$$

Mā te whakawehe ki te -780 ka wetekia te whakareanga ki te -780.

$$x^{2}+\left(-\frac{151}{-780}\right)x=\frac{0}{-780}$$

Whakawehe -151 ki te -780.

$$x^{2}+\frac{151}{780}x=\frac{0}{-780}$$

Whakawehe 0 ki te -780.

$$x^{2}+\frac{151}{780}x=0$$

Whakawehea te \frac{151}{780}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{151}{1560}. Nā, tāpiria te pūrua o te \frac{151}{1560} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{151}{780}x+\left(\frac{151}{1560}\right)^{2}=\left(\frac{151}{1560}\right)^{2}$$

Pūruatia \frac{151}{1560} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{151}{780}x+\frac{22801}{2433600}=\frac{22801}{2433600}$$

Tauwehea x^{2}+\frac{151}{780}x+\frac{22801}{2433600}. 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}.

$$\left(x+\frac{151}{1560}\right)^{2}=\frac{22801}{2433600}$$

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

$$\sqrt{\left(x+\frac{151}{1560}\right)^{2}}=\sqrt{\frac{22801}{2433600}}$$

Whakarūnātia.

$$x+\frac{151}{1560}=\frac{151}{1560} x+\frac{151}{1560}=-\frac{151}{1560}$$

Me tango \frac{151}{1560} mai i ngā taha e rua o te whārite.

$$x=0 x=-\frac{151}{780}$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=-\frac{151}{780}$$