Whakaoti i te (x-11)(x-085)+015*01=0

$$( x - 11 ) ( x - 085 ) + 015 \times 01 = 0$$

Whakaoti mō x

$$x=0$$

$$x=11$$

Ngā Upane Whakamahi Tauwehe

Whakareatia te 0 ki te 85, ka 0.

$$\left(x-11\right)\left(x-0\right)+0\times 15\times 0\times 1=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-11 ki te x-0.

$$x\left(x-0\right)-11\left(x-0\right)+0\times 15\times 0\times 1=0$$

Whakareatia te 0 ki te 15, ka 0.

$$x\left(x-0\right)-11\left(x-0\right)+0\times 0\times 1=0$$

Whakareatia te 0 ki te 0, ka 0.

$$x\left(x-0\right)-11\left(x-0\right)+0\times 1=0$$

Whakareatia te 0 ki te 1, ka 0.

$$x\left(x-0\right)-11\left(x-0\right)+0=0$$

Ko te tau i tāpiria he kore ka hua koia tonu.

$$x\left(x-0\right)-11\left(x-0\right)=0$$

Whakaraupapatia anō ngā kīanga tau.

$$xx-11x=0$$

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

$$x^{2}-11x=0$$

Tauwehea te x.

$$x\left(x-11\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te x-11=0.

$$x=0 x=11$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 0 ki te 85, ka 0.

$$\left(x-11\right)\left(x-0\right)+0\times 15\times 0\times 1=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-11 ki te x-0.

$$x\left(x-0\right)-11\left(x-0\right)+0\times 15\times 0\times 1=0$$

Whakareatia te 0 ki te 15, ka 0.

$$x\left(x-0\right)-11\left(x-0\right)+0\times 0\times 1=0$$

Whakareatia te 0 ki te 0, ka 0.

$$x\left(x-0\right)-11\left(x-0\right)+0\times 1=0$$

Whakareatia te 0 ki te 1, ka 0.

$$x\left(x-0\right)-11\left(x-0\right)+0=0$$

Ko te tau i tāpiria he kore ka hua koia tonu.

$$x\left(x-0\right)-11\left(x-0\right)=0$$

Whakaraupapatia anō ngā kīanga tau.

$$xx-11x=0$$

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

$$x^{2}-11x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -11 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-11\right)±\sqrt{\left(-11\right)^{2}}}{2}$$

Tuhia te pūtakerua o te \left(-11\right)^{2}.

$$x=\frac{-\left(-11\right)±11}{2}$$

Ko te tauaro o -11 ko 11.

$$x=\frac{11±11}{2}$$

Nā, me whakaoti te whārite x=\frac{11±11}{2} ina he tāpiri te ±. Tāpiri 11 ki te 11.

$$x=\frac{22}{2}$$

Whakawehe 22 ki te 2.

$$x=11$$

Nā, me whakaoti te whārite x=\frac{11±11}{2} ina he tango te ±. Tango 11 mai i 11.

$$x=\frac{0}{2}$$

Whakawehe 0 ki te 2.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=11 x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te 0 ki te 85, ka 0.

$$\left(x-11\right)\left(x-0\right)+0\times 15\times 0\times 1=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-11 ki te x-0.

$$x\left(x-0\right)-11\left(x-0\right)+0\times 15\times 0\times 1=0$$

Whakareatia te 0 ki te 15, ka 0.

$$x\left(x-0\right)-11\left(x-0\right)+0\times 0\times 1=0$$

Whakareatia te 0 ki te 0, ka 0.

$$x\left(x-0\right)-11\left(x-0\right)+0\times 1=0$$

Whakareatia te 0 ki te 1, ka 0.

$$x\left(x-0\right)-11\left(x-0\right)+0=0$$

Ko te tau i tāpiria he kore ka hua koia tonu.

$$x\left(x-0\right)-11\left(x-0\right)=0$$

Whakaraupapatia anō ngā kīanga tau.

$$xx-11x=0$$

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

$$x^{2}-11x=0$$

Whakawehea te -11, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{11}{2}. Nā, tāpiria te pūrua o te -\frac{11}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-11x+\left(-\frac{11}{2}\right)^{2}=\left(-\frac{11}{2}\right)^{2}$$

Pūruatia -\frac{11}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-11x+\frac{121}{4}=\frac{121}{4}$$

Tauwehea x^{2}-11x+\frac{121}{4}. 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}.

$$\left(x-\frac{11}{2}\right)^{2}=\frac{121}{4}$$

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

$$\sqrt{\left(x-\frac{11}{2}\right)^{2}}=\sqrt{\frac{121}{4}}$$

Whakarūnātia.

$$x-\frac{11}{2}=\frac{11}{2} x-\frac{11}{2}=-\frac{11}{2}$$

Me tāpiri \frac{11}{2} ki ngā taha e rua o te whārite.

$$x=11 x=0$$