Whakaoti i te x*(-20x+920)=3100

$$x \cdot ( - 20 x + 920 ) = 3100$$

Whakaoti mō x

$$x=\sqrt{374}+23\approx 42.339079606$$

$$x=23-\sqrt{374}\approx 3.660920394$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te -20x+920.

$$-20x^{2}+920x=3100$$

Tangohia te 3100 mai i ngā taha e rua.

$$-20x^{2}+920x-3100=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -20 mō a, 920 mō b, me -3100 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-920±\sqrt{920^{2}-4\left(-20\right)\left(-3100\right)}}{2\left(-20\right)}$$

Pūrua 920.

$$x=\frac{-920±\sqrt{846400-4\left(-20\right)\left(-3100\right)}}{2\left(-20\right)}$$

Whakareatia -4 ki te -20.

$$x=\frac{-920±\sqrt{846400+80\left(-3100\right)}}{2\left(-20\right)}$$

Whakareatia 80 ki te -3100.

$$x=\frac{-920±\sqrt{846400-248000}}{2\left(-20\right)}$$

Tāpiri 846400 ki te -248000.

$$x=\frac{-920±\sqrt{598400}}{2\left(-20\right)}$$

Tuhia te pūtakerua o te 598400.

$$x=\frac{-920±40\sqrt{374}}{2\left(-20\right)}$$

Whakareatia 2 ki te -20.

$$x=\frac{-920±40\sqrt{374}}{-40}$$

Nā, me whakaoti te whārite x=\frac{-920±40\sqrt{374}}{-40} ina he tāpiri te ±. Tāpiri -920 ki te 40\sqrt{374}.

$$x=\frac{40\sqrt{374}-920}{-40}$$

Whakawehe -920+40\sqrt{374} ki te -40.

$$x=23-\sqrt{374}$$

Nā, me whakaoti te whārite x=\frac{-920±40\sqrt{374}}{-40} ina he tango te ±. Tango 40\sqrt{374} mai i -920.

$$x=\frac{-40\sqrt{374}-920}{-40}$$

Whakawehe -920-40\sqrt{374} ki te -40.

$$x=\sqrt{374}+23$$

Kua oti te whārite te whakatau.

$$x=23-\sqrt{374} x=\sqrt{374}+23$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te -20x+920.

$$-20x^{2}+920x=3100$$

Whakawehea ngā taha e rua ki te -20.

$$\frac{-20x^{2}+920x}{-20}=\frac{3100}{-20}$$

Mā te whakawehe ki te -20 ka wetekia te whakareanga ki te -20.

$$x^{2}+\frac{920}{-20}x=\frac{3100}{-20}$$

Whakawehe 920 ki te -20.

$$x^{2}-46x=\frac{3100}{-20}$$

Whakawehe 3100 ki te -20.

$$x^{2}-46x=-155$$

Whakawehea te -46, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -23. Nā, tāpiria te pūrua o te -23 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-46x+\left(-23\right)^{2}=-155+\left(-23\right)^{2}$$

Pūrua -23.

$$x^{2}-46x+529=-155+529$$

Tāpiri -155 ki te 529.

$$x^{2}-46x+529=374$$

Tauwehea x^{2}-46x+529. 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}.

$$\left(x-23\right)^{2}=374$$

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

$$\sqrt{\left(x-23\right)^{2}}=\sqrt{374}$$

Whakarūnātia.

$$x-23=\sqrt{374} x-23=-\sqrt{374}$$

Me tāpiri 23 ki ngā taha e rua o te whārite.

$$x=\sqrt{374}+23 x=23-\sqrt{374}$$