Whakaoti i te x^2+2584=106x

$${ x }^{ 2 } +2584=106x$$

Whakaoti mō x

$$x=38$$

$$x=68$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 106x mai i ngā taha e rua.

$$x^{2}+2584-106x=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$x^{2}-106x+2584=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -106 mō b, me 2584 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-106\right)±\sqrt{\left(-106\right)^{2}-4\times 2584}}{2}$$

Pūrua -106.

$$x=\frac{-\left(-106\right)±\sqrt{11236-4\times 2584}}{2}$$

Whakareatia -4 ki te 2584.

$$x=\frac{-\left(-106\right)±\sqrt{11236-10336}}{2}$$

Tāpiri 11236 ki te -10336.

$$x=\frac{-\left(-106\right)±\sqrt{900}}{2}$$

Tuhia te pūtakerua o te 900.

$$x=\frac{-\left(-106\right)±30}{2}$$

Ko te tauaro o -106 ko 106.

$$x=\frac{106±30}{2}$$

Nā, me whakaoti te whārite x=\frac{106±30}{2} ina he tāpiri te ±. Tāpiri 106 ki te 30.

$$x=\frac{136}{2}$$

Whakawehe 136 ki te 2.

$$x=68$$

Nā, me whakaoti te whārite x=\frac{106±30}{2} ina he tango te ±. Tango 30 mai i 106.

$$x=\frac{76}{2}$$

Whakawehe 76 ki te 2.

$$x=38$$

Kua oti te whārite te whakatau.

$$x=68 x=38$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 106x mai i ngā taha e rua.

$$x^{2}+2584-106x=0$$

Tangohia te 2584 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x^{2}-106x=-2584$$

Whakawehea te -106, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -53. Nā, tāpiria te pūrua o te -53 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-106x+\left(-53\right)^{2}=-2584+\left(-53\right)^{2}$$

Pūrua -53.

$$x^{2}-106x+2809=-2584+2809$$

Tāpiri -2584 ki te 2809.

$$x^{2}-106x+2809=225$$

Tauwehea x^{2}-106x+2809. 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}.

$$\left(x-53\right)^{2}=225$$

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

$$\sqrt{\left(x-53\right)^{2}}=\sqrt{225}$$

Whakarūnātia.

$$x-53=15 x-53=-15$$

Me tāpiri 53 ki ngā taha e rua o te whārite.

$$x=68 x=38$$