Whakaoti i te 16x^2+40x+25=4x^2+40x+100

$$16 { x }^{ 2 } +40x+25=4 { x }^{ 2 } +40x+100$$

Whakaoti mō x

$$x = -\frac{5}{2} = -2\frac{1}{2} = -2.5$$

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Tangohia te 4x^{2} mai i ngā taha e rua.

$$16x^{2}+40x+25-4x^{2}=40x+100$$

Pahekotia te 16x^{2} me -4x^{2}, ka 12x^{2}.

$$12x^{2}+40x+25=40x+100$$

Tangohia te 40x mai i ngā taha e rua.

$$12x^{2}+40x+25-40x=100$$

Pahekotia te 40x me -40x, ka 0.

$$12x^{2}+25=100$$

Tangohia te 100 mai i ngā taha e rua.

$$12x^{2}+25-100=0$$

Tangohia te 100 i te 25, ka -75.

$$12x^{2}-75=0$$

Whakawehea ngā taha e rua ki te 3.

$$4x^{2}-25=0$$

Whakaarohia te 4x^{2}-25. Tuhia anō te 4x^{2}-25 hei \left(2x\right)^{2}-5^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2x-5\right)\left(2x+5\right)=0$$

Hei kimi otinga whārite, me whakaoti te 2x-5=0 me te 2x+5=0.

$$x=\frac{5}{2} x=-\frac{5}{2}$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 4x^{2} mai i ngā taha e rua.

$$16x^{2}+40x+25-4x^{2}=40x+100$$

Pahekotia te 16x^{2} me -4x^{2}, ka 12x^{2}.

$$12x^{2}+40x+25=40x+100$$

Tangohia te 40x mai i ngā taha e rua.

$$12x^{2}+40x+25-40x=100$$

Pahekotia te 40x me -40x, ka 0.

$$12x^{2}+25=100$$

Tangohia te 25 mai i ngā taha e rua.

$$12x^{2}=100-25$$

Tangohia te 25 i te 100, ka 75.

$$12x^{2}=75$$

Whakawehea ngā taha e rua ki te 12.

$$x^{2}=\frac{75}{12}$$

Whakahekea te hautanga \frac{75}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$x^{2}=\frac{25}{4}$$

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

$$x=\frac{5}{2} x=-\frac{5}{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 4x^{2} mai i ngā taha e rua.

$$16x^{2}+40x+25-4x^{2}=40x+100$$

Pahekotia te 16x^{2} me -4x^{2}, ka 12x^{2}.

$$12x^{2}+40x+25=40x+100$$

Tangohia te 40x mai i ngā taha e rua.

$$12x^{2}+40x+25-40x=100$$

Pahekotia te 40x me -40x, ka 0.

$$12x^{2}+25=100$$

Tangohia te 100 mai i ngā taha e rua.

$$12x^{2}+25-100=0$$

Tangohia te 100 i te 25, ka -75.

$$12x^{2}-75=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 12 mō a, 0 mō b, me -75 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 12\left(-75\right)}}{2\times 12}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 12\left(-75\right)}}{2\times 12}$$

Whakareatia -4 ki te 12.

$$x=\frac{0±\sqrt{-48\left(-75\right)}}{2\times 12}$$

Whakareatia -48 ki te -75.

$$x=\frac{0±\sqrt{3600}}{2\times 12}$$

Tuhia te pūtakerua o te 3600.

$$x=\frac{0±60}{2\times 12}$$

Whakareatia 2 ki te 12.

$$x=\frac{0±60}{24}$$

Nā, me whakaoti te whārite x=\frac{0±60}{24} ina he tāpiri te ±. Whakahekea te hautanga \frac{60}{24} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 12.

$$x=\frac{5}{2}$$

Nā, me whakaoti te whārite x=\frac{0±60}{24} ina he tango te ±. Whakahekea te hautanga \frac{-60}{24} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 12.

$$x=-\frac{5}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{5}{2} x=-\frac{5}{2}$$